36y2-24y=85

Solution for 36y2-24y=85 equation:

36y^2-24y=85

We move all terms to the left:

36y^2-24y-(85)=0

a = 36; b = -24; c = -85;
Δ = b2-4ac
Δ = -242-4·36·(-85)
Δ = 12816
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:

$\sqrt{\Delta}=\sqrt{12816}=\sqrt{144*89}=\sqrt{144}*\sqrt{89}=12\sqrt{89}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-24)-12\sqrt{89}}{2*36}=\frac{24-12\sqrt{89}}{72}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-24)+12\sqrt{89}}{2*36}=\frac{24+12\sqrt{89}}{72}
$