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

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

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

We move all terms to the left:

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

We multiply parentheses

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


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

-11+4(x+4)

determiningTheFunctionDomain
4(x+4)-11

We multiply parentheses

4x+16-11

We add all the numbers together, and all the variables

4x+5

Back to the equation:

-(4x+5)


We get rid of parentheses

-2x^2-12x-4x-5+3=0

We add all the numbers together, and all the variables

-2x^2-16x-2=0

a = -2; b = -16; c = -2;
Δ = b2-4ac
Δ = -162-4·(-2)·(-2)
Δ = 240
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:

$\sqrt{\Delta}=\sqrt{240}=\sqrt{16*15}=\sqrt{16}*\sqrt{15}=4\sqrt{15}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-16)-4\sqrt{15}}{2*-2}=\frac{16-4\sqrt{15}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-16)+4\sqrt{15}}{2*-2}=\frac{16+4\sqrt{15}}{-4}
$