7/8x+1/2=3/16x-5

Solution for 7/8x+1/2=3/16x-5 equation:

7/8x+1/2=3/16x-5

We move all terms to the left:

7/8x+1/2-(3/16x-5)=0


Domain of the equation: 8x!=0

x!=0/8

x!=0

x∈R



Domain of the equation: 16x-5)!=0

x∈R


We get rid of parentheses

7/8x-3/16x+5+1/2=0

We calculate fractions


128x^2/512x^2+448x/512x^2+(-96x)/512x^2+5=0

We multiply all the terms by the denominator


128x^2+448x+(-96x)+5*512x^2=0

Wy multiply elements

128x^2+2560x^2+448x+(-96x)=0

We get rid of parentheses

128x^2+2560x^2+448x-96x=0

We add all the numbers together, and all the variables

2688x^2+352x=0

a = 2688; b = 352; c = 0;
Δ = b2-4ac
Δ = 3522-4·2688·0
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*2688}=\frac{-704}{5376}
=-11/84
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(352)+352}{2*2688}=\frac{0}{5376}
=0
$