13/5x+18=24/7x-36

Solution for 13/5x+18=24/7x-36 equation:

13/5x+18=24/7x-36

We move all terms to the left:

13/5x+18-(24/7x-36)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R



Domain of the equation: 7x-36)!=0

x∈R


We get rid of parentheses

13/5x-24/7x+36+18=0

We calculate fractions


91x/35x^2+(-120x)/35x^2+36+18=0

We add all the numbers together, and all the variables

91x/35x^2+(-120x)/35x^2+54=0

We multiply all the terms by the denominator


91x+(-120x)+54*35x^2=0

Wy multiply elements

1890x^2+91x+(-120x)=0

We get rid of parentheses

1890x^2+91x-120x=0

We add all the numbers together, and all the variables

1890x^2-29x=0

a = 1890; b = -29; c = 0;
Δ = b2-4ac
Δ = -292-4·1890·0
Δ = 841
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{841}=29$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-29)-29}{2*1890}=\frac{0}{3780}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-29)+29}{2*1890}=\frac{58}{3780}
=29/1890
$