2x(3x-1)=5-(x+3)

Solution for 2x(3x-1)=5-(x+3) equation:

2x(3x-1)=5-(x+3)

We move all terms to the left:

2x(3x-1)-(5-(x+3))=0

We multiply parentheses

6x^2-2x-(5-(x+3))=0


We calculate terms in parentheses: -(5-(x+3)), so:

5-(x+3)

determiningTheFunctionDomain
-(x+3)+5

We get rid of parentheses

-x-3+5

We add all the numbers together, and all the variables

-1x+2

Back to the equation:

-(-1x+2)


We get rid of parentheses

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

We add all the numbers together, and all the variables

6x^2-1x-2=0

a = 6; b = -1; c = -2;
Δ = b2-4ac
Δ = -12-4·6·(-2)
Δ = 49
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{49}=7$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-7}{2*6}=\frac{-6}{12}
=-1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+7}{2*6}=\frac{8}{12}
=2/3
$