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

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

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

We move all terms to the left:

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

We add all the numbers together, and all the variables

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

We multiply parentheses

-2x^2-8x-(6(x+2)+3x)=0


We calculate terms in parentheses: -(6(x+2)+3x), so:

6(x+2)+3x

We add all the numbers together, and all the variables

3x+6(x+2)

We multiply parentheses

3x+6x+12

We add all the numbers together, and all the variables

9x+12

Back to the equation:

-(9x+12)


We get rid of parentheses

-2x^2-8x-9x-12=0

We add all the numbers together, and all the variables

-2x^2-17x-12=0

a = -2; b = -17; c = -12;
Δ = b2-4ac
Δ = -172-4·(-2)·(-12)
Δ = 193
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{-(-17)-\sqrt{193}}{2*-2}=\frac{17-\sqrt{193}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-17)+\sqrt{193}}{2*-2}=\frac{17+\sqrt{193}}{-4}
$