2/3x+4=32-4x

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

2/3x+4=32-4x

We move all terms to the left:

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


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

2/3x+4x-32+4=0

We multiply all the terms by the denominator


4x*3x-32*3x+4*3x+2=0

Wy multiply elements

12x^2-96x+12x+2=0

We add all the numbers together, and all the variables

12x^2-84x+2=0

a = 12; b = -84; c = +2;
Δ = b2-4ac
Δ = -842-4·12·2
Δ = 6960
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{6960}=\sqrt{16*435}=\sqrt{16}*\sqrt{435}=4\sqrt{435}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-84)-4\sqrt{435}}{2*12}=\frac{84-4\sqrt{435}}{24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-84)+4\sqrt{435}}{2*12}=\frac{84+4\sqrt{435}}{24}
$