Y=6x^2+36x-5

Solution for Y=6x^2+36x-5 equation:

=6Y^2+36Y-5

We move all terms to the left:

-(6Y^2+36Y-5)=0

We get rid of parentheses

-6Y^2-36Y+5=0

a = -6; b = -36; c = +5;
Δ = b2-4ac
Δ = -362-4·(-6)·5
Δ = 1416
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{1416}=\sqrt{4*354}=\sqrt{4}*\sqrt{354}=2\sqrt{354}$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-36)-2\sqrt{354}}{2*-6}=\frac{36-2\sqrt{354}}{-12}
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-36)+2\sqrt{354}}{2*-6}=\frac{36+2\sqrt{354}}{-12}
$