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

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

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

We move all terms to the left:

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

We multiply parentheses

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


We calculate terms in parentheses: -(2x(x+4)+2), so:

2x(x+4)+2

We multiply parentheses

2x^2+8x+2

Back to the equation:

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


We get rid of parentheses

x^2-2x^2-3x-8x-2=0

We add all the numbers together, and all the variables

-1x^2-11x-2=0

a = -1; b = -11; c = -2;
Δ = b2-4ac
Δ = -112-4·(-1)·(-2)
Δ = 113
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{-(-11)-\sqrt{113}}{2*-1}=\frac{11-\sqrt{113}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-11)+\sqrt{113}}{2*-1}=\frac{11+\sqrt{113}}{-2}
$