2h+(6/h-4)=6h-5.2

Solution for 2h+(6/h-4)=6h-5.2 equation:

2h+(6/h-4)=6h-5.2

We move all terms to the left:

2h+(6/h-4)-(6h-5.2)=0


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

h∈R


We get rid of parentheses

2h+6/h-6h-4+5.2=0

We multiply all the terms by the denominator


2h*h-6h*h-4*h+(5.2)*h+6=0

We add all the numbers together, and all the variables

-4h+2h*h-6h*h+(5.2)*h+6=0

We multiply parentheses

-4h+2h*h-6h*h+5.2h+6=0

Wy multiply elements

2h^2-6h^2-4h+5.2h+6=0

We add all the numbers together, and all the variables

-4h^2+1.2h+6=0

a = -4; b = 1.2; c = +6;
Δ = b2-4ac
Δ = 1.22-4·(-4)·6
Δ = 97.44
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{-(1.2)-\sqrt{97.44}}{2*-4}=\frac{-1.2-\sqrt{97.44}}{-8}
$
$h_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1.2)+\sqrt{97.44}}{2*-4}=\frac{-1.2+\sqrt{97.44}}{-8}
$