3/4*h-5=1/4*h-1

Solution for 3/4*h-5=1/4*h-1 equation:

3/4*h-5=1/4*h-1

We move all terms to the left:

3/4*h-5-(1/4*h-1)=0


Domain of the equation: 4*h!=0

h!=0/1

h!=0

h∈R



Domain of the equation: 4*h-1)!=0

h∈R


We get rid of parentheses

3/4*h-1/4*h+1-5=0

We multiply all the terms by the denominator


1*4*h-5*4*h+3-1=0

We add all the numbers together, and all the variables

1*4*h-5*4*h+2=0

Wy multiply elements

4h*h-20h*h+2=0

Wy multiply elements

4h^2-20h^2+2=0

We add all the numbers together, and all the variables

-16h^2+2=0

a = -16; b = 0; c = +2;
Δ = b2-4ac
Δ = 02-4·(-16)·2
Δ = 128
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:

$\sqrt{\Delta}=\sqrt{128}=\sqrt{64*2}=\sqrt{64}*\sqrt{2}=8\sqrt{2}$
$h_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-8\sqrt{2}}{2*-16}=\frac{0-8\sqrt{2}}{-32}
=-\frac{8\sqrt{2}}{-32}
=-\frac{\sqrt{2}}{-4}
$
$h_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+8\sqrt{2}}{2*-16}=\frac{0+8\sqrt{2}}{-32}
=\frac{8\sqrt{2}}{-32}
=\frac{\sqrt{2}}{-4}
$