3x+2(x2)=13-(2x+2)

Solution for 3x+2(x2)=13-(2x+2) equation:

3x+2(x2)=13-(2x+2)

We move all terms to the left:

3x+2(x2)-(13-(2x+2))=0

We add all the numbers together, and all the variables

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


We calculate terms in parentheses: -(13-(2x+2)), so:

13-(2x+2)

determiningTheFunctionDomain
-(2x+2)+13

We get rid of parentheses

-2x-2+13

We add all the numbers together, and all the variables

-2x+11

Back to the equation:

-(-2x+11)


We get rid of parentheses

2x^2+3x+2x-11=0

We add all the numbers together, and all the variables

2x^2+5x-11=0

a = 2; b = 5; c = -11;
Δ = b2-4ac
Δ = 52-4·2·(-11)
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{-(5)-\sqrt{113}}{2*2}=\frac{-5-\sqrt{113}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+\sqrt{113}}{2*2}=\frac{-5+\sqrt{113}}{4}
$