3/4x-1/3x=-15/8

Solution for 3/4x-1/3x=-15/8 equation:

3/4x-1/3x=-15/8

We move all terms to the left:

3/4x-1/3x-(-15/8)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R



Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We get rid of parentheses

3/4x-1/3x+15/8=0

We calculate fractions


540x^2/768x^2+576x/768x^2+(-256x)/768x^2=0

We multiply all the terms by the denominator


540x^2+576x+(-256x)=0

We get rid of parentheses

540x^2+576x-256x=0

We add all the numbers together, and all the variables

540x^2+320x=0

a = 540; b = 320; c = 0;
Δ = b2-4ac
Δ = 3202-4·540·0
Δ = 102400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{102400}=320$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(320)-320}{2*540}=\frac{-640}{1080}
=-16/27
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(320)+320}{2*540}=\frac{0}{1080}
=0
$