4(2x2-2)-2x=5-(3x+4)

Solution for 4(2x2-2)-2x=5-(3x+4) equation:

4(2x^2-2)-2x=5-(3x+4)

We move all terms to the left:

4(2x^2-2)-2x-(5-(3x+4))=0

We add all the numbers together, and all the variables

-2x+4(2x^2-2)-(5-(3x+4))=0

We multiply parentheses

8x^2-2x-(5-(3x+4))-8=0


We calculate terms in parentheses: -(5-(3x+4)), so:

5-(3x+4)

determiningTheFunctionDomain
-(3x+4)+5

We get rid of parentheses

-3x-4+5

We add all the numbers together, and all the variables

-3x+1

Back to the equation:

-(-3x+1)


We get rid of parentheses

8x^2-2x+3x-1-8=0

We add all the numbers together, and all the variables

8x^2+x-9=0

a = 8; b = 1; c = -9;
Δ = b2-4ac
Δ = 12-4·8·(-9)
Δ = 289
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{289}=17$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-17}{2*8}=\frac{-18}{16}
=-1+1/8
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+17}{2*8}=\frac{16}{16}
=1
$