6/5h-3=2/h-7

Solution for 6/5h-3=2/h-7 equation:

6/5h-3=2/h-7

We move all terms to the left:

6/5h-3-(2/h-7)=0


Domain of the equation: 5h!=0

h!=0/5

h!=0

h∈R



Domain of the equation: h-7)!=0

h∈R


We get rid of parentheses

6/5h-2/h+7-3=0

We calculate fractions


6h/5h^2+(-10h)/5h^2+7-3=0

We add all the numbers together, and all the variables

6h/5h^2+(-10h)/5h^2+4=0

We multiply all the terms by the denominator


6h+(-10h)+4*5h^2=0

Wy multiply elements

20h^2+6h+(-10h)=0

We get rid of parentheses

20h^2+6h-10h=0

We add all the numbers together, and all the variables

20h^2-4h=0

a = 20; b = -4; c = 0;
Δ = b2-4ac
Δ = -42-4·20·0
Δ = 16
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$h_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$h_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{16}=4$
$h_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-4}{2*20}=\frac{0}{40}
=0
$
$h_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+4}{2*20}=\frac{8}{40}
=1/5
$