Y=5x+6x^2

Solution for Y=5x+6x^2 equation:

=5Y+6Y^2

We move all terms to the left:

-(5Y+6Y^2)=0

We get rid of parentheses

-6Y^2-5Y=0

a = -6; b = -5; c = 0;
Δ = b2-4ac
Δ = -52-4·(-6)·0
Δ = 25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{25}=5$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-5}{2*-6}=\frac{0}{-12}
=0
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+5}{2*-6}=\frac{10}{-12}
=-5/6
$