.5(h-1)(h)=15

Solution for .5(h-1)(h)=15 equation:

.5(h-1)(h)=15

We move all terms to the left:

.5(h-1)(h)-(15)=0

We multiply parentheses

0h^2+0h-15=0

We add all the numbers together, and all the variables

h^2+h-15=0

a = 1; b = 1; c = -15;
Δ = b2-4ac
Δ = 12-4·1·(-15)
Δ = 61
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$h_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$h_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$h_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-\sqrt{61}}{2*1}=\frac{-1-\sqrt{61}}{2}
$
$h_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+\sqrt{61}}{2*1}=\frac{-1+\sqrt{61}}{2}
$