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

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

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

We move all terms to the left:

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

We add all the numbers together, and all the variables

-1x+2x(x+3)-(-x-4(x+2))=0

We multiply parentheses

2x^2-1x+6x-(-x-4(x+2))=0


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

-x-4(x+2)

We add all the numbers together, and all the variables

-1x-4(x+2)

We multiply parentheses

-1x-4x-8

We add all the numbers together, and all the variables

-5x-8

Back to the equation:

-(-5x-8)


We add all the numbers together, and all the variables

2x^2+5x-(-5x-8)=0

We get rid of parentheses

2x^2+5x+5x+8=0

We add all the numbers together, and all the variables

2x^2+10x+8=0

a = 2; b = 10; c = +8;
Δ = b2-4ac
Δ = 102-4·2·8
Δ = 36
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{36}=6$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-6}{2*2}=\frac{-16}{4}
=-4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+6}{2*2}=\frac{-4}{4}
=-1
$