2x(-7+3x)=5-(x+2)

Solution for 2x(-7+3x)=5-(x+2) equation:

2x(-7+3x)=5-(x+2)

We move all terms to the left:

2x(-7+3x)-(5-(x+2))=0

We add all the numbers together, and all the variables

2x(3x-7)-(5-(x+2))=0

We multiply parentheses

6x^2-14x-(5-(x+2))=0


We calculate terms in parentheses: -(5-(x+2)), so:

5-(x+2)

determiningTheFunctionDomain
-(x+2)+5

We get rid of parentheses

-x-2+5

We add all the numbers together, and all the variables

-1x+3

Back to the equation:

-(-1x+3)


We get rid of parentheses

6x^2-14x+1x-3=0

We add all the numbers together, and all the variables

6x^2-13x-3=0

a = 6; b = -13; c = -3;
Δ = b2-4ac
Δ = -132-4·6·(-3)
Δ = 241
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{-(-13)-\sqrt{241}}{2*6}=\frac{13-\sqrt{241}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-13)+\sqrt{241}}{2*6}=\frac{13+\sqrt{241}}{12}
$