4*(15*h*1/2)=500

Solution for 4*(15*h*1/2)=500 equation:

4(15h*1/2)=500

We move all terms to the left:

4(15h*1/2)-(500)=0

We add all the numbers together, and all the variables

4(+15h*1/2)-500=0

We multiply parentheses

60h^2-500=0

a = 60; b = 0; c = -500;
Δ = b2-4ac
Δ = 02-4·60·(-500)
Δ = 120000
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:

$\sqrt{\Delta}=\sqrt{120000}=\sqrt{40000*3}=\sqrt{40000}*\sqrt{3}=200\sqrt{3}$
$h_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-200\sqrt{3}}{2*60}=\frac{0-200\sqrt{3}}{120}
=-\frac{200\sqrt{3}}{120}
=-\frac{5\sqrt{3}}{3}
$
$h_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+200\sqrt{3}}{2*60}=\frac{0+200\sqrt{3}}{120}
=\frac{200\sqrt{3}}{120}
=\frac{5\sqrt{3}}{3}
$