-7/8x+1/6=2/3x+5

Solution for -7/8x+1/6=2/3x+5 equation:

-7/8x+1/6=2/3x+5

We move all terms to the left:

-7/8x+1/6-(2/3x+5)=0


Domain of the equation: 8x!=0

x!=0/8

x!=0

x∈R



Domain of the equation: 3x+5)!=0

x∈R


We get rid of parentheses

-7/8x-2/3x-5+1/6=0

We calculate fractions


72x^2/864x^2+(-756x)/864x^2+(-576x)/864x^2-5=0

We multiply all the terms by the denominator


72x^2+(-756x)+(-576x)-5*864x^2=0

Wy multiply elements

72x^2-4320x^2+(-756x)+(-576x)=0

We get rid of parentheses

72x^2-4320x^2-756x-576x=0

We add all the numbers together, and all the variables

-4248x^2-1332x=0

a = -4248; b = -1332; c = 0;
Δ = b2-4ac
Δ = -13322-4·(-4248)·0
Δ = 1774224
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1774224}=1332$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1332)-1332}{2*-4248}=\frac{0}{-8496}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1332)+1332}{2*-4248}=\frac{2664}{-8496}
=-37/118
$