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

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

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

We move all terms to the left:

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


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R



Domain of the equation: 4x+4)!=0

x∈R


We get rid of parentheses

4/3x-3/4x-4-2=0

We calculate fractions


16x/12x^2+(-9x)/12x^2-4-2=0

We add all the numbers together, and all the variables

16x/12x^2+(-9x)/12x^2-6=0

We multiply all the terms by the denominator


16x+(-9x)-6*12x^2=0

Wy multiply elements

-72x^2+16x+(-9x)=0

We get rid of parentheses

-72x^2+16x-9x=0

We add all the numbers together, and all the variables

-72x^2+7x=0

a = -72; b = 7; c = 0;
Δ = b2-4ac
Δ = 72-4·(-72)·0
Δ = 49
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{49}=7$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(7)-7}{2*-72}=\frac{-14}{-144}
=7/72
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+7}{2*-72}=\frac{0}{-144}
=0
$