-2(x+6)+3=-11x(x+4)

Solution for -2(x+6)+3=-11x(x+4) equation:

-2(x+6)+3=-11x(x+4)

We move all terms to the left:

-2(x+6)+3-(-11x(x+4))=0

We multiply parentheses

-2x-(-11x(x+4))-12+3=0


We calculate terms in parentheses: -(-11x(x+4)), so:

-11x(x+4)

We multiply parentheses

-11x^2-44x

Back to the equation:

-(-11x^2-44x)


We add all the numbers together, and all the variables

-(-11x^2-44x)-2x-9=0

We get rid of parentheses

11x^2+44x-2x-9=0

We add all the numbers together, and all the variables

11x^2+42x-9=0

a = 11; b = 42; c = -9;
Δ = b2-4ac
Δ = 422-4·11·(-9)
Δ = 2160
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:

$\sqrt{\Delta}=\sqrt{2160}=\sqrt{144*15}=\sqrt{144}*\sqrt{15}=12\sqrt{15}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(42)-12\sqrt{15}}{2*11}=\frac{-42-12\sqrt{15}}{22}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(42)+12\sqrt{15}}{2*11}=\frac{-42+12\sqrt{15}}{22}
$