39=0.5(h-7)h

Solution for 39=0.5(h-7)h equation:

39=0.5(h-7)h

We move all terms to the left:

39-(0.5(h-7)h)=0


We calculate terms in parentheses: -(0.5(h-7)h), so:

0.5(h-7)h

We multiply parentheses

0h^2+0h

We add all the numbers together, and all the variables

h^2+h

Back to the equation:

-(h^2+h)


We get rid of parentheses

-h^2-h+39=0

We add all the numbers together, and all the variables

-1h^2-1h+39=0

a = -1; b = -1; c = +39;
Δ = b2-4ac
Δ = -12-4·(-1)·39
Δ = 157
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{157}}{2*-1}=\frac{1-\sqrt{157}}{-2}
$
$h_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+\sqrt{157}}{2*-1}=\frac{1+\sqrt{157}}{-2}
$