108/5x+2=144/7x

Solution for 108/5x+2=144/7x equation:

108/5x+2=144/7x

We move all terms to the left:

108/5x+2-(144/7x)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R



Domain of the equation: 7x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

108/5x-(+144/7x)+2=0

We get rid of parentheses

108/5x-144/7x+2=0

We calculate fractions


756x/35x^2+(-720x)/35x^2+2=0

We multiply all the terms by the denominator


756x+(-720x)+2*35x^2=0

Wy multiply elements

70x^2+756x+(-720x)=0

We get rid of parentheses

70x^2+756x-720x=0

We add all the numbers together, and all the variables

70x^2+36x=0

a = 70; b = 36; c = 0;
Δ = b2-4ac
Δ = 362-4·70·0
Δ = 1296
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1296}=36$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(36)-36}{2*70}=\frac{-72}{140}
=-18/35
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(36)+36}{2*70}=\frac{0}{140}
=0
$