3(x2-1)+7=6x-3-2(2-4x)

Solution for 3(x2-1)+7=6x-3-2(2-4x) equation:

3(x2-1)+7=6x-3-2(2-4x)

We move all terms to the left:

3(x2-1)+7-(6x-3-2(2-4x))=0

We add all the numbers together, and all the variables

3(+x^2-1)-(6x-3-2(-4x+2))+7=0

We multiply parentheses

3x^2-(6x-3-2(-4x+2))-3+7=0


We calculate terms in parentheses: -(6x-3-2(-4x+2)), so:

6x-3-2(-4x+2)

determiningTheFunctionDomain
6x-2(-4x+2)-3

We multiply parentheses

6x+8x-4-3

We add all the numbers together, and all the variables

14x-7

Back to the equation:

-(14x-7)


We add all the numbers together, and all the variables

3x^2-(14x-7)+4=0

We get rid of parentheses

3x^2-14x+7+4=0

We add all the numbers together, and all the variables

3x^2-14x+11=0

a = 3; b = -14; c = +11;
Δ = b2-4ac
Δ = -142-4·3·11
Δ = 64
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{64}=8$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-14)-8}{2*3}=\frac{6}{6}
=1
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-14)+8}{2*3}=\frac{22}{6}
=3+2/3
$