2y(y+5)=10

Solution for 2y(y+5)=10 equation:

2y(y+5)=10

We move all terms to the left:

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

We multiply parentheses

2y^2+10y-10=0

a = 2; b = 10; c = -10;
Δ = b2-4ac
Δ = 102-4·2·(-10)
Δ = 180
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:

$\sqrt{\Delta}=\sqrt{180}=\sqrt{36*5}=\sqrt{36}*\sqrt{5}=6\sqrt{5}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-6\sqrt{5}}{2*2}=\frac{-10-6\sqrt{5}}{4}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+6\sqrt{5}}{2*2}=\frac{-10+6\sqrt{5}}{4}
$