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

Solution for 13-x(2x+2)=2(x+2)+3x equation:

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

We move all terms to the left:

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

We multiply parentheses

-2x^2-2x-(2(x+2)+3x)+13=0


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

2(x+2)+3x

We add all the numbers together, and all the variables

3x+2(x+2)

We multiply parentheses

3x+2x+4

We add all the numbers together, and all the variables

5x+4

Back to the equation:

-(5x+4)


We get rid of parentheses

-2x^2-2x-5x-4+13=0

We add all the numbers together, and all the variables

-2x^2-7x+9=0

a = -2; b = -7; c = +9;
Δ = b2-4ac
Δ = -72-4·(-2)·9
Δ = 121
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{121}=11$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-7)-11}{2*-2}=\frac{-4}{-4}
=1
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+11}{2*-2}=\frac{18}{-4}
=-4+1/2
$