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

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

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

We move all terms to the left:

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


Domain of the equation: 3x+2)!=0

x∈R


We multiply parentheses

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

We get rid of parentheses

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

We multiply all the terms by the denominator


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

Wy multiply elements

12x^2-6x-12x-2=0

We add all the numbers together, and all the variables

12x^2-18x-2=0

a = 12; b = -18; c = -2;
Δ = b2-4ac
Δ = -182-4·12·(-2)
Δ = 420
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:

$\sqrt{\Delta}=\sqrt{420}=\sqrt{4*105}=\sqrt{4}*\sqrt{105}=2\sqrt{105}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-18)-2\sqrt{105}}{2*12}=\frac{18-2\sqrt{105}}{24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-18)+2\sqrt{105}}{2*12}=\frac{18+2\sqrt{105}}{24}
$