8/3x-9/4x=-52/12

Solution for 8/3x-9/4x=-52/12 equation:

8/3x-9/4x=-52/12

We move all terms to the left:

8/3x-9/4x-(-52/12)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R



Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R


We get rid of parentheses

8/3x-9/4x+52/12=0

We calculate fractions


2496x^2/144x^2+384x/144x^2+(-324x)/144x^2=0

We multiply all the terms by the denominator


2496x^2+384x+(-324x)=0

We get rid of parentheses

2496x^2+384x-324x=0

We add all the numbers together, and all the variables

2496x^2+60x=0

a = 2496; b = 60; c = 0;
Δ = b2-4ac
Δ = 602-4·2496·0
Δ = 3600
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{3600}=60$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(60)-60}{2*2496}=\frac{-120}{4992}
=-5/208
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(60)+60}{2*2496}=\frac{0}{4992}
=0
$