(3h*h)/2=75

Solution for (3h*h)/2=75 equation:

(3h*h)/2=75

We move all terms to the left:

(3h*h)/2-(75)=0

We add all the numbers together, and all the variables

(+3h*h)/2-75=0

We multiply all the terms by the denominator


(+3h*h)-75*2=0

We add all the numbers together, and all the variables

(+3h*h)-150=0

We get rid of parentheses

3h*h-150=0

Wy multiply elements

3h^2-150=0

a = 3; b = 0; c = -150;
Δ = b2-4ac
Δ = 02-4·3·(-150)
Δ = 1800
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:

$\sqrt{\Delta}=\sqrt{1800}=\sqrt{900*2}=\sqrt{900}*\sqrt{2}=30\sqrt{2}$
$h_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-30\sqrt{2}}{2*3}=\frac{0-30\sqrt{2}}{6}
=-\frac{30\sqrt{2}}{6}
=-5\sqrt{2}
$
$h_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+30\sqrt{2}}{2*3}=\frac{0+30\sqrt{2}}{6}
=\frac{30\sqrt{2}}{6}
=5\sqrt{2}
$