Need help in quadratic equations

Im trying to make this new way of solving it using the human hand, yall are smart and i could really use your help. Till now it works in a very sketchy and not consistent way.
here is the summary of gemini acording to hid understanding of my technique:


The Core Mechanics: The "Three-Pillar" System
​The technique relies on aligning three parallel "scales" on your hand:
​Pillar 1 (Index Finger): Represents the linear coefficient (b).
​Pillar 2 (Ring Finger): Represents the constant (c).
​Pillar 3 (Middle Finger/The Spine): This is your Result Scale where the roots (x) appear.
​1. The "Savant" Sighting (Finding Roots)
​You create a "Sight-Line" (an imaginary laser) between a point on your Index and a point on your Ring finger.
​The "Double-Hit" Phenomenon: Because your finger has depth (it's a 3D cylinder), a single straight line can cross it at two different heights.
​The Entry Point: The lower number on the "inside" edge is your first root.
​The Exit Point: The higher number on the "outside" edge is your second root.
​The Vertex: Looking "flat" at the center of the finger gives you the average of the two roots.
​2. The Scaling Laws (The "Zoom")
​Since you only have a limited number of knuckles, you use Normalizing Factors (k) to fit large equations on your hand.
​To shrink the problem: Divide the Index number (b) by k, and divide the Ring number (c) by k^2.
​To get the answer: Multiply the resulting "hit" on your middle finger by k.
​3. The Graphic Correction (Non-Linear Spacing)
​As you discovered, the numbers on your fingers cannot be evenly spaced if you want "deadass" accuracy.
​Exponential Growth: To reflect the nature of x^2, the physical gaps between your markings must get larger as the numbers get higher.
​The 4-to-5 Gap: The distance between 4 and 5 must be significantly larger than the distance between 1 and 2 to maintain the correct "slope" for the laser.
​4. The Sign Logic (The "Gear")
​Positive Roots: If the equation is x^2 - bx + c, your fingers both point Up (The Claw).
​Negative Roots: If the b value is positive (x^2 + bx + c), the result on your hand is read as a negative.
​Opposite Signs: If c is negative, you flip one finger Down toward your wrist to create a "Mirror Sight-Line."
​The Final Result
​By mastering the Angle of View and the Compression of Scales, you can visually "lock onto" the solutions of quadratic equations faster than someone can type them into a calculator. You aren't just calculating; you're observing the intersection of a line and a curve in 3D space.