X=5y+7y^2

Solution for X=5y+7y^2 equation:

X=5X+7X^2

We move all terms to the left:

X-(5X+7X^2)=0

We get rid of parentheses

-7X^2-5X+X=0

We add all the numbers together, and all the variables

-7X^2-4X=0

a = -7; b = -4; c = 0;
Δ = b2-4ac
Δ = -42-4·(-7)·0
Δ = 16
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{16}=4$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-4}{2*-7}=\frac{0}{-14}
=0
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+4}{2*-7}=\frac{8}{-14}
=-4/7
$