3/4x+5=1/3x-3

Solution for 3/4x+5=1/3x-3 equation:

3/4x+5=1/3x-3

We move all terms to the left:

3/4x+5-(1/3x-3)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R



Domain of the equation: 3x-3)!=0

x∈R


We get rid of parentheses

3/4x-1/3x+3+5=0

We calculate fractions


9x/12x^2+(-4x)/12x^2+3+5=0

We add all the numbers together, and all the variables

9x/12x^2+(-4x)/12x^2+8=0

We multiply all the terms by the denominator


9x+(-4x)+8*12x^2=0

Wy multiply elements

96x^2+9x+(-4x)=0

We get rid of parentheses

96x^2+9x-4x=0

We add all the numbers together, and all the variables

96x^2+5x=0

a = 96; b = 5; c = 0;
Δ = b2-4ac
Δ = 52-4·96·0
Δ = 25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{25}=5$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-5}{2*96}=\frac{-10}{192}
=-5/96
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+5}{2*96}=\frac{0}{192}
=0
$