1/5h-3(2/5h-2)=2/5h-8

Solution for 1/5h-3(2/5h-2)=2/5h-8 equation:

1/5h-3(2/5h-2)=2/5h-8

We move all terms to the left:

1/5h-3(2/5h-2)-(2/5h-8)=0


Domain of the equation: 5h!=0

h!=0/5

h!=0

h∈R



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

h∈R



Domain of the equation: 5h-8)!=0

h∈R


We multiply parentheses

1/5h-6h-(2/5h-8)+6=0

We get rid of parentheses

1/5h-6h-2/5h+8+6=0

We multiply all the terms by the denominator


-6h*5h+8*5h+6*5h+1-2=0

We add all the numbers together, and all the variables

-6h*5h+8*5h+6*5h-1=0

Wy multiply elements

-30h^2+40h+30h-1=0

We add all the numbers together, and all the variables

-30h^2+70h-1=0

a = -30; b = 70; c = -1;
Δ = b2-4ac
Δ = 702-4·(-30)·(-1)
Δ = 4780
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:

$\sqrt{\Delta}=\sqrt{4780}=\sqrt{4*1195}=\sqrt{4}*\sqrt{1195}=2\sqrt{1195}$
$h_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(70)-2\sqrt{1195}}{2*-30}=\frac{-70-2\sqrt{1195}}{-60}
$
$h_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(70)+2\sqrt{1195}}{2*-30}=\frac{-70+2\sqrt{1195}}{-60}
$