5y^2+30y=-15

Solution for 5y^2+30y=-15 equation:

5y^2+30y=-15

We move all terms to the left:

5y^2+30y-(-15)=0

We add all the numbers together, and all the variables

5y^2+30y+15=0

a = 5; b = 30; c = +15;
Δ = b2-4ac
Δ = 302-4·5·15
Δ = 600
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:

$\sqrt{\Delta}=\sqrt{600}=\sqrt{100*6}=\sqrt{100}*\sqrt{6}=10\sqrt{6}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(30)-10\sqrt{6}}{2*5}=\frac{-30-10\sqrt{6}}{10}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(30)+10\sqrt{6}}{2*5}=\frac{-30+10\sqrt{6}}{10}
$