X=8y^2-12

Solution for X=8y^2-12 equation:

X=8X^2-12

We move all terms to the left:

X-(8X^2-12)=0

We get rid of parentheses

-8X^2+X+12=0

a = -8; b = 1; c = +12;
Δ = b2-4ac
Δ = 12-4·(-8)·12
Δ = 385
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-\sqrt{385}}{2*-8}=\frac{-1-\sqrt{385}}{-16}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+\sqrt{385}}{2*-8}=\frac{-1+\sqrt{385}}{-16}
$