5y^2+10y=10

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

5y^2+10y=10

We move all terms to the left:

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

a = 5; b = 10; c = -10;
Δ = b2-4ac
Δ = 102-4·5·(-10)
Δ = 300
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:

$\sqrt{\Delta}=\sqrt{300}=\sqrt{100*3}=\sqrt{100}*\sqrt{3}=10\sqrt{3}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-10\sqrt{3}}{2*5}=\frac{-10-10\sqrt{3}}{10}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+10\sqrt{3}}{2*5}=\frac{-10+10\sqrt{3}}{10}
$