h-3=4/5h-2

Solution for h-3=4/5h-2 equation:

h-3=4/5h-2

We move all terms to the left:

h-3-(4/5h-2)=0


Domain of the equation: 5h-2)!=0

h∈R


We get rid of parentheses

h-4/5h+2-3=0

We multiply all the terms by the denominator


h*5h+2*5h-3*5h-4=0

Wy multiply elements

5h^2+10h-15h-4=0

We add all the numbers together, and all the variables

5h^2-5h-4=0

a = 5; b = -5; c = -4;
Δ = b2-4ac
Δ = -52-4·5·(-4)
Δ = 105
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$h_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$h_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$h_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-\sqrt{105}}{2*5}=\frac{5-\sqrt{105}}{10}
$
$h_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+\sqrt{105}}{2*5}=\frac{5+\sqrt{105}}{10}
$