7/8x-1=-15/16x+5

Solution for 7/8x-1=-15/16x+5 equation:

7/8x-1=-15/16x+5

We move all terms to the left:

7/8x-1-(-15/16x+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+15/16x-5-1=0

We calculate fractions


112x/128x^2+120x/128x^2-5-1=0

We add all the numbers together, and all the variables

112x/128x^2+120x/128x^2-6=0

We multiply all the terms by the denominator


112x+120x-6*128x^2=0

We add all the numbers together, and all the variables

232x-6*128x^2=0

Wy multiply elements

-768x^2+232x=0

a = -768; b = 232; c = 0;
Δ = b2-4ac
Δ = 2322-4·(-768)·0
Δ = 53824
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{53824}=232$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(232)-232}{2*-768}=\frac{-464}{-1536}
=29/96
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(232)+232}{2*-768}=\frac{0}{-1536}
=0
$