0.5h^2+h=4h

Solution for 0.5h^2+h=4h equation:

0.5h^2+h=4h

We move all terms to the left:

0.5h^2+h-(4h)=0

We add all the numbers together, and all the variables

0.5h^2-3h=0

a = 0.5; b = -3; c = 0;
Δ = b2-4ac
Δ = -32-4·0.5·0
Δ = 9
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$h_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$h_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{9}=3$
$h_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3)-3}{2*0.5}=\frac{0}{1}
=0
$
$h_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+3}{2*0.5}=\frac{6}{1}
=6
$