10y^2-10y+5y+60=180

Solution for 10y^2-10y+5y+60=180 equation:

10y^2-10y+5y+60=180

We move all terms to the left:

10y^2-10y+5y+60-(180)=0

We add all the numbers together, and all the variables

10y^2-5y-120=0

a = 10; b = -5; c = -120;
Δ = b2-4ac
Δ = -52-4·10·(-120)
Δ = 4825
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:

$\sqrt{\Delta}=\sqrt{4825}=\sqrt{25*193}=\sqrt{25}*\sqrt{193}=5\sqrt{193}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-5\sqrt{193}}{2*10}=\frac{5-5\sqrt{193}}{20}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+5\sqrt{193}}{2*10}=\frac{5+5\sqrt{193}}{20}
$