x(x-1)+x=4(x+2)

Solution for x(x-1)+x=4(x+2) equation:

x(x-1)+x=4(x+2)

We move all terms to the left:

x(x-1)+x-(4(x+2))=0

We add all the numbers together, and all the variables

x+x(x-1)-(4(x+2))=0

We multiply parentheses

x^2+x-1x-(4(x+2))=0


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

4(x+2)

We multiply parentheses

4x+8

Back to the equation:

-(4x+8)


We add all the numbers together, and all the variables

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

We get rid of parentheses

x^2-4x-8=0

a = 1; b = -4; c = -8;
Δ = b2-4ac
Δ = -42-4·1·(-8)
Δ = 48
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{48}=\sqrt{16*3}=\sqrt{16}*\sqrt{3}=4\sqrt{3}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-4\sqrt{3}}{2*1}=\frac{4-4\sqrt{3}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+4\sqrt{3}}{2*1}=\frac{4+4\sqrt{3}}{2}
$