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

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

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

We move all terms to the left:

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

We multiply parentheses

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

We get rid of parentheses

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

We multiply all the terms by the denominator


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

We add all the numbers together, and all the variables

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

Wy multiply elements

6x^2-1x+24x-3x+3=0

We add all the numbers together, and all the variables

6x^2+20x+3=0

a = 6; b = 20; c = +3;
Δ = b2-4ac
Δ = 202-4·6·3
Δ = 328
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:

$\sqrt{\Delta}=\sqrt{328}=\sqrt{4*82}=\sqrt{4}*\sqrt{82}=2\sqrt{82}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(20)-2\sqrt{82}}{2*6}=\frac{-20-2\sqrt{82}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(20)+2\sqrt{82}}{2*6}=\frac{-20+2\sqrt{82}}{12}
$