20y+73+y2=180

Solution for 20y+73+y2=180 equation:

20y+73+y2=180

We move all terms to the left:

20y+73+y2-(180)=0

We add all the numbers together, and all the variables

y^2+20y-107=0

a = 1; b = 20; c = -107;
Δ = b2-4ac
Δ = 202-4·1·(-107)
Δ = 828
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:

$\sqrt{\Delta}=\sqrt{828}=\sqrt{36*23}=\sqrt{36}*\sqrt{23}=6\sqrt{23}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(20)-6\sqrt{23}}{2*1}=\frac{-20-6\sqrt{23}}{2}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(20)+6\sqrt{23}}{2*1}=\frac{-20+6\sqrt{23}}{2}
$