5/7x-8=2/13x+5

Solution for 5/7x-8=2/13x+5 equation:

5/7x-8=2/13x+5

We move all terms to the left:

5/7x-8-(2/13x+5)=0


Domain of the equation: 7x!=0

x!=0/7

x!=0

x∈R



Domain of the equation: 13x+5)!=0

x∈R


We get rid of parentheses

5/7x-2/13x-5-8=0

We calculate fractions


65x/91x^2+(-14x)/91x^2-5-8=0

We add all the numbers together, and all the variables

65x/91x^2+(-14x)/91x^2-13=0

We multiply all the terms by the denominator


65x+(-14x)-13*91x^2=0

Wy multiply elements

-1183x^2+65x+(-14x)=0

We get rid of parentheses

-1183x^2+65x-14x=0

We add all the numbers together, and all the variables

-1183x^2+51x=0

a = -1183; b = 51; c = 0;
Δ = b2-4ac
Δ = 512-4·(-1183)·0
Δ = 2601
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2601}=51$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(51)-51}{2*-1183}=\frac{-102}{-2366}
=51/1183
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(51)+51}{2*-1183}=\frac{0}{-2366}
=0
$