3/4x-2=5/8x+3

Solution for 3/4x-2=5/8x+3 equation:

3/4x-2=5/8x+3

We move all terms to the left:

3/4x-2-(5/8x+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-5/8x-3-2=0

We calculate fractions


24x/32x^2+(-20x)/32x^2-3-2=0

We add all the numbers together, and all the variables

24x/32x^2+(-20x)/32x^2-5=0

We multiply all the terms by the denominator


24x+(-20x)-5*32x^2=0

Wy multiply elements

-160x^2+24x+(-20x)=0

We get rid of parentheses

-160x^2+24x-20x=0

We add all the numbers together, and all the variables

-160x^2+4x=0

a = -160; b = 4; c = 0;
Δ = b2-4ac
Δ = 42-4·(-160)·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*-160}=\frac{-8}{-320}
=1/40
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+4}{2*-160}=\frac{0}{-320}
=0
$