2x-2x(6x+5)=(3x-2)(4x+1)

Solution for 2x-2x(6x+5)=(3x-2)(4x+1) equation:

2x-2x(6x+5)=(3x-2)(4x+1)

We move all terms to the left:

2x-2x(6x+5)-((3x-2)(4x+1))=0

We multiply parentheses

-12x^2+2x-10x-((3x-2)(4x+1))=0

We multiply parentheses ..

-12x^2-((+12x^2+3x-8x-2))+2x-10x=0


We calculate terms in parentheses: -((+12x^2+3x-8x-2)), so:

(+12x^2+3x-8x-2)

We get rid of parentheses

12x^2+3x-8x-2

We add all the numbers together, and all the variables

12x^2-5x-2

Back to the equation:

-(12x^2-5x-2)


We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

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

a = -24; b = -3; c = +2;
Δ = b2-4ac
Δ = -32-4·(-24)·2
Δ = 201
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{-(-3)-\sqrt{201}}{2*-24}=\frac{3-\sqrt{201}}{-48}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+\sqrt{201}}{2*-24}=\frac{3+\sqrt{201}}{-48}
$