y=-12X^2-2X+4

Solution for y=-12X^2-2X+4 equation:

y=-12y^2-2y+4

We move all terms to the left:

y-(-12y^2-2y+4)=0

We get rid of parentheses

12y^2+2y+y-4=0

We add all the numbers together, and all the variables

12y^2+3y-4=0

a = 12; b = 3; c = -4;
Δ = b2-4ac
Δ = 32-4·12·(-4)
Δ = 201
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(3)-\sqrt{201}}{2*12}=\frac{-3-\sqrt{201}}{24}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+\sqrt{201}}{2*12}=\frac{-3+\sqrt{201}}{24}
$