2(1/2x+4)-1=4/3x-3+x

Solution for 2(1/2x+4)-1=4/3x-3+x equation:

2(1/2x+4)-1=4/3x-3+x

We move all terms to the left:

2(1/2x+4)-1-(4/3x-3+x)=0


Domain of the equation: 2x+4)!=0

x∈R



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

We move all terms containing x to the left, all other terms to the right

3x+x)!=3

x∈R


We add all the numbers together, and all the variables

2(1/2x+4)-(x+4/3x-3)-1=0

We multiply parentheses

2x-(x+4/3x-3)+8-1=0

We get rid of parentheses

2x-x-4/3x+3+8-1=0

We multiply all the terms by the denominator


2x*3x-x*3x+3*3x+8*3x-1*3x-4=0

Wy multiply elements

6x^2-3x^2+9x+24x-3x-4=0

We add all the numbers together, and all the variables

3x^2+30x-4=0

a = 3; b = 30; c = -4;
Δ = b2-4ac
Δ = 302-4·3·(-4)
Δ = 948
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:

$\sqrt{\Delta}=\sqrt{948}=\sqrt{4*237}=\sqrt{4}*\sqrt{237}=2\sqrt{237}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(30)-2\sqrt{237}}{2*3}=\frac{-30-2\sqrt{237}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(30)+2\sqrt{237}}{2*3}=\frac{-30+2\sqrt{237}}{6}
$