10=2h^2+10h

Solution for 10=2h^2+10h equation:

10=2h^2+10h

We move all terms to the left:

10-(2h^2+10h)=0

We get rid of parentheses

-2h^2-10h+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:
$h_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$h_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

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