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

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

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

We move all terms to the left:

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


Domain of the equation: 7x!=0

x!=0/7

x!=0

x∈R



Domain of the equation: 8x+7)!=0

x∈R


We get rid of parentheses

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

We calculate fractions


40x/56x^2+(-35x)/56x^2-7-3=0

We add all the numbers together, and all the variables

40x/56x^2+(-35x)/56x^2-10=0

We multiply all the terms by the denominator


40x+(-35x)-10*56x^2=0

Wy multiply elements

-560x^2+40x+(-35x)=0

We get rid of parentheses

-560x^2+40x-35x=0

We add all the numbers together, and all the variables

-560x^2+5x=0

a = -560; b = 5; c = 0;
Δ = b2-4ac
Δ = 52-4·(-560)·0
Δ = 25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{25}=5$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-5}{2*-560}=\frac{-10}{-1120}
=1/112
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+5}{2*-560}=\frac{0}{-1120}
=0
$