-2(6x+1)=-11x(x-2)

Solution for -2(6x+1)=-11x(x-2) equation:

-2(6x+1)=-11x(x-2)

We move all terms to the left:

-2(6x+1)-(-11x(x-2))=0

We multiply parentheses

-12x-(-11x(x-2))-2=0


We calculate terms in parentheses: -(-11x(x-2)), so:

-11x(x-2)

We multiply parentheses

-11x^2+22x

Back to the equation:

-(-11x^2+22x)


We get rid of parentheses

11x^2-22x-12x-2=0

We add all the numbers together, and all the variables

11x^2-34x-2=0

a = 11; b = -34; c = -2;
Δ = b2-4ac
Δ = -342-4·11·(-2)
Δ = 1244
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:

$\sqrt{\Delta}=\sqrt{1244}=\sqrt{4*311}=\sqrt{4}*\sqrt{311}=2\sqrt{311}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-34)-2\sqrt{311}}{2*11}=\frac{34-2\sqrt{311}}{22}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-34)+2\sqrt{311}}{2*11}=\frac{34+2\sqrt{311}}{22}
$