8x-(3x-2)=4x(3x-1)-4x

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Solution for 8x-(3x-2)=4x(3x-1)-4x equation: 



8x-(3x-2)=4x(3x-1)-4x

We move all terms to the left:

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

We get rid of parentheses

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



We calculate terms in parentheses: -(4x(3x-1)-4x), so:

4x(3x-1)-4x

We add all the numbers together, and all the variables

-4x+4x(3x-1)

We multiply parentheses

12x^2-4x-4x

We add all the numbers together, and all the variables

12x^2-8x

Back to the equation:

-(12x^2-8x)



We add all the numbers together, and all the variables

5x-(12x^2-8x)+2=0

We get rid of parentheses

-12x^2+5x+8x+2=0

We add all the numbers together, and all the variables

-12x^2+13x+2=0

a = -12; b = 13; c = +2;
Δ = b2-4ac
Δ = 132-4·(-12)·2
Δ = 265
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{-(13)-\sqrt{265}}{2*-12}=\frac{-13-\sqrt{265}}{-24}
$


$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(13)+\sqrt{265}}{2*-12}=\frac{-13+\sqrt{265}}{-24}
$

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