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

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

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

We move all terms to the left:

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


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R



Domain of the equation: 8x+3)!=0

x∈R


We get rid of parentheses

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

We calculate fractions


24x/32x^2+28x/32x^2-3-2=0

We add all the numbers together, and all the variables

24x/32x^2+28x/32x^2-5=0

We multiply all the terms by the denominator


24x+28x-5*32x^2=0

We add all the numbers together, and all the variables

52x-5*32x^2=0

Wy multiply elements

-160x^2+52x=0

a = -160; b = 52; c = 0;
Δ = b2-4ac
Δ = 522-4·(-160)·0
Δ = 2704
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2704}=52$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(52)-52}{2*-160}=\frac{-104}{-320}
=13/40
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(52)+52}{2*-160}=\frac{0}{-320}
=0
$