7/8x-32=3/4x+32

Solution for 7/8x-32=3/4x+32 equation:

7/8x-32=3/4x+32

We move all terms to the left:

7/8x-32-(3/4x+32)=0


Domain of the equation: 8x!=0

x!=0/8

x!=0

x∈R



Domain of the equation: 4x+32)!=0

x∈R


We get rid of parentheses

7/8x-3/4x-32-32=0

We calculate fractions


28x/32x^2+(-24x)/32x^2-32-32=0

We add all the numbers together, and all the variables

28x/32x^2+(-24x)/32x^2-64=0

We multiply all the terms by the denominator


28x+(-24x)-64*32x^2=0

Wy multiply elements

-2048x^2+28x+(-24x)=0

We get rid of parentheses

-2048x^2+28x-24x=0

We add all the numbers together, and all the variables

-2048x^2+4x=0

a = -2048; b = 4; c = 0;
Δ = b2-4ac
Δ = 42-4·(-2048)·0
Δ = 16
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{16}=4$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-4}{2*-2048}=\frac{-8}{-4096}
=1/512
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+4}{2*-2048}=\frac{0}{-4096}
=0
$