3/4x=7/8x-2

Solution for 3/4x=7/8x-2 equation:

3/4x=7/8x-2

We move all terms to the left:

3/4x-(7/8x-2)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R



Domain of the equation: 8x-2)!=0

x∈R


We get rid of parentheses

3/4x-7/8x+2=0

We calculate fractions


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

We multiply all the terms by the denominator


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

Wy multiply elements

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

We get rid of parentheses

64x^2+24x-28x=0

We add all the numbers together, and all the variables

64x^2-4x=0

a = 64; b = -4; c = 0;
Δ = b2-4ac
Δ = -42-4·64·0
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*64}=\frac{0}{128}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+4}{2*64}=\frac{8}{128}
=1/16
$