5y^2-15=10y+15

Solution for 5y^2-15=10y+15 equation:

5y^2-15=10y+15

We move all terms to the left:

5y^2-15-(10y+15)=0

We get rid of parentheses

5y^2-10y-15-15=0

We add all the numbers together, and all the variables

5y^2-10y-30=0

a = 5; b = -10; c = -30;
Δ = b2-4ac
Δ = -102-4·5·(-30)
Δ = 700
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:

$\sqrt{\Delta}=\sqrt{700}=\sqrt{100*7}=\sqrt{100}*\sqrt{7}=10\sqrt{7}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-10\sqrt{7}}{2*5}=\frac{10-10\sqrt{7}}{10}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+10\sqrt{7}}{2*5}=\frac{10+10\sqrt{7}}{10}
$