7/8x-1/2=3/16x+6

Solution for 7/8x-1/2=3/16x+6 equation:

7/8x-1/2=3/16x+6

We move all terms to the left:

7/8x-1/2-(3/16x+6)=0


Domain of the equation: 8x!=0

x!=0/8

x!=0

x∈R



Domain of the equation: 16x+6)!=0

x∈R


We get rid of parentheses

7/8x-3/16x-6-1/2=0

We calculate fractions


(-128x^2)/512x^2+448x/512x^2+(-96x)/512x^2-6=0

We multiply all the terms by the denominator


(-128x^2)+448x+(-96x)-6*512x^2=0

Wy multiply elements

(-128x^2)-3072x^2+448x+(-96x)=0

We get rid of parentheses

-128x^2-3072x^2+448x-96x=0

We add all the numbers together, and all the variables

-3200x^2+352x=0

a = -3200; b = 352; c = 0;
Δ = b2-4ac
Δ = 3522-4·(-3200)·0
Δ = 123904
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{123904}=352$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(352)-352}{2*-3200}=\frac{-704}{-6400}
=11/100
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(352)+352}{2*-3200}=\frac{0}{-6400}
=0
$