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

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

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

We move all terms to the left:

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


Domain of the equation: 8x!=0

x!=0/8

x!=0

x∈R



Domain of the equation: 1x+5)!=0

x∈R


We get rid of parentheses

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

We calculate fractions


(-8x^2)/32x^2+28x/32x^2+(-96x)/32x^2-5=0

We multiply all the terms by the denominator


(-8x^2)+28x+(-96x)-5*32x^2=0

Wy multiply elements

(-8x^2)-160x^2+28x+(-96x)=0

We get rid of parentheses

-8x^2-160x^2+28x-96x=0

We add all the numbers together, and all the variables

-168x^2-68x=0

a = -168; b = -68; c = 0;
Δ = b2-4ac
Δ = -682-4·(-168)·0
Δ = 4624
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4624}=68$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-68)-68}{2*-168}=\frac{0}{-336}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-68)+68}{2*-168}=\frac{136}{-336}
=-17/42
$