y^2-3y=135

Solution for y^2-3y=135 equation:

y^2-3y=135

We move all terms to the left:

y^2-3y-(135)=0

a = 1; b = -3; c = -135;
Δ = b2-4ac
Δ = -32-4·1·(-135)
Δ = 549
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:

$\sqrt{\Delta}=\sqrt{549}=\sqrt{9*61}=\sqrt{9}*\sqrt{61}=3\sqrt{61}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3)-3\sqrt{61}}{2*1}=\frac{3-3\sqrt{61}}{2}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+3\sqrt{61}}{2*1}=\frac{3+3\sqrt{61}}{2}
$