(3/4)h=45/50

Solution for (3/4)h=45/50 equation:

(3/4)h=45/50

We move all terms to the left:

(3/4)h-(45/50)=0


Domain of the equation: 4)h!=0

h!=0/1

h!=0

h∈R


We add all the numbers together, and all the variables

(+3/4)h-(+45/50)=0

We multiply parentheses

3h^2-(+45/50)=0

We get rid of parentheses

3h^2-45/50=0

We multiply all the terms by the denominator


3h^2*50-45=0

Wy multiply elements

150h^2-45=0

a = 150; b = 0; c = -45;
Δ = b2-4ac
Δ = 02-4·150·(-45)
Δ = 27000
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:

$\sqrt{\Delta}=\sqrt{27000}=\sqrt{900*30}=\sqrt{900}*\sqrt{30}=30\sqrt{30}$
$h_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-30\sqrt{30}}{2*150}=\frac{0-30\sqrt{30}}{300}
=-\frac{30\sqrt{30}}{300}
=-\frac{\sqrt{30}}{10}
$
$h_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+30\sqrt{30}}{2*150}=\frac{0+30\sqrt{30}}{300}
=\frac{30\sqrt{30}}{300}
=\frac{\sqrt{30}}{10}
$