7/8x-1/2=3/7x+5

Solution for 7/8x-1/2=3/7x+5 equation:

7/8x-1/2=3/7x+5

We move all terms to the left:

7/8x-1/2-(3/7x+5)=0


Domain of the equation: 8x!=0

x!=0/8

x!=0

x∈R



Domain of the equation: 7x+5)!=0

x∈R


We get rid of parentheses

7/8x-3/7x-5-1/2=0

We calculate fractions


(-392x^2)/224x^2+196x/224x^2+(-96x)/224x^2-5=0

We multiply all the terms by the denominator


(-392x^2)+196x+(-96x)-5*224x^2=0

Wy multiply elements

(-392x^2)-1120x^2+196x+(-96x)=0

We get rid of parentheses

-392x^2-1120x^2+196x-96x=0

We add all the numbers together, and all the variables

-1512x^2+100x=0

a = -1512; b = 100; c = 0;
Δ = b2-4ac
Δ = 1002-4·(-1512)·0
Δ = 10000
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{10000}=100$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(100)-100}{2*-1512}=\frac{-200}{-3024}
=25/378
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(100)+100}{2*-1512}=\frac{0}{-3024}
=0
$