4x(x-4)+2=x2+2(2x+17)

Solution for 4x(x-4)+2=x2+2(2x+17) equation:

4x(x-4)+2=x2+2(2x+17)

We move all terms to the left:

4x(x-4)+2-(x2+2(2x+17))=0

We multiply parentheses

4x^2-16x-(x2+2(2x+17))+2=0


We calculate terms in parentheses: -(x2+2(2x+17)), so:

x2+2(2x+17)

We add all the numbers together, and all the variables

x^2+2(2x+17)

We multiply parentheses

x^2+4x+34

Back to the equation:

-(x^2+4x+34)


We get rid of parentheses

4x^2-x^2-16x-4x-34+2=0

We add all the numbers together, and all the variables

3x^2-20x-32=0

a = 3; b = -20; c = -32;
Δ = b2-4ac
Δ = -202-4·3·(-32)
Δ = 784
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{784}=28$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-20)-28}{2*3}=\frac{-8}{6}
=-1+1/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-20)+28}{2*3}=\frac{48}{6}
=8
$