4/3x-2(13x+32)=2x-13

Solution for 4/3x-2(13x+32)=2x-13 equation:

4/3x-2(13x+32)=2x-13

We move all terms to the left:

4/3x-2(13x+32)-(2x-13)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We multiply parentheses

4/3x-26x-(2x-13)-64=0

We get rid of parentheses

4/3x-26x-2x+13-64=0

We multiply all the terms by the denominator


-26x*3x-2x*3x+13*3x-64*3x+4=0

Wy multiply elements

-78x^2-6x^2+39x-192x+4=0

We add all the numbers together, and all the variables

-84x^2-153x+4=0

a = -84; b = -153; c = +4;
Δ = b2-4ac
Δ = -1532-4·(-84)·4
Δ = 24753
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-153)-\sqrt{24753}}{2*-84}=\frac{153-\sqrt{24753}}{-168}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-153)+\sqrt{24753}}{2*-84}=\frac{153+\sqrt{24753}}{-168}
$