12x-6x(x+1)=4(2x-1)-3

Solution for 12x-6x(x+1)=4(2x-1)-3 equation:

12x-6x(x+1)=4(2x-1)-3

We move all terms to the left:

12x-6x(x+1)-(4(2x-1)-3)=0

We multiply parentheses

-6x^2+12x-6x-(4(2x-1)-3)=0


We calculate terms in parentheses: -(4(2x-1)-3), so:

4(2x-1)-3

We multiply parentheses

8x-4-3

We add all the numbers together, and all the variables

8x-7

Back to the equation:

-(8x-7)


We add all the numbers together, and all the variables

-6x^2+6x-(8x-7)=0

We get rid of parentheses

-6x^2+6x-8x+7=0

We add all the numbers together, and all the variables

-6x^2-2x+7=0

a = -6; b = -2; c = +7;
Δ = b2-4ac
Δ = -22-4·(-6)·7
Δ = 172
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:

$\sqrt{\Delta}=\sqrt{172}=\sqrt{4*43}=\sqrt{4}*\sqrt{43}=2\sqrt{43}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-2\sqrt{43}}{2*-6}=\frac{2-2\sqrt{43}}{-12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+2\sqrt{43}}{2*-6}=\frac{2+2\sqrt{43}}{-12}
$