8y-15+y2=180

Solution for 8y-15+y2=180 equation:

8y-15+y2=180

We move all terms to the left:

8y-15+y2-(180)=0

We add all the numbers together, and all the variables

y^2+8y-195=0

a = 1; b = 8; c = -195;
Δ = b2-4ac
Δ = 82-4·1·(-195)
Δ = 844
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:

$\sqrt{\Delta}=\sqrt{844}=\sqrt{4*211}=\sqrt{4}*\sqrt{211}=2\sqrt{211}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-2\sqrt{211}}{2*1}=\frac{-8-2\sqrt{211}}{2}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+2\sqrt{211}}{2*1}=\frac{-8+2\sqrt{211}}{2}
$