7/8x-3=15/16x+2

Solution for 7/8x-3=15/16x+2 equation:

7/8x-3=15/16x+2

We move all terms to the left:

7/8x-3-(15/16x+2)=0


Domain of the equation: 8x!=0

x!=0/8

x!=0

x∈R



Domain of the equation: 16x+2)!=0

x∈R


We get rid of parentheses

7/8x-15/16x-2-3=0

We calculate fractions


112x/128x^2+(-120x)/128x^2-2-3=0

We add all the numbers together, and all the variables

112x/128x^2+(-120x)/128x^2-5=0

We multiply all the terms by the denominator


112x+(-120x)-5*128x^2=0

Wy multiply elements

-640x^2+112x+(-120x)=0

We get rid of parentheses

-640x^2+112x-120x=0

We add all the numbers together, and all the variables

-640x^2-8x=0

a = -640; b = -8; c = 0;
Δ = b2-4ac
Δ = -82-4·(-640)·0
Δ = 64
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{64}=8$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-8}{2*-640}=\frac{0}{-1280}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+8}{2*-640}=\frac{16}{-1280}
=-1/80
$