X=2y^2+12y+10

Solution for X=2y^2+12y+10 equation:

X=2X^2+12X+10

We move all terms to the left:

X-(2X^2+12X+10)=0

We get rid of parentheses

-2X^2+X-12X-10=0

We add all the numbers together, and all the variables

-2X^2-11X-10=0

a = -2; b = -11; c = -10;
Δ = b2-4ac
Δ = -112-4·(-2)·(-10)
Δ = 41
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{-(-11)-\sqrt{41}}{2*-2}=\frac{11-\sqrt{41}}{-4}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-11)+\sqrt{41}}{2*-2}=\frac{11+\sqrt{41}}{-4}
$