2x(x-6)+2=4(x+2)-12

Solution for 2x(x-6)+2=4(x+2)-12 equation:

2x(x-6)+2=4(x+2)-12

We move all terms to the left:

2x(x-6)+2-(4(x+2)-12)=0

We multiply parentheses

2x^2-12x-(4(x+2)-12)+2=0


We calculate terms in parentheses: -(4(x+2)-12), so:

4(x+2)-12

We multiply parentheses

4x+8-12

We add all the numbers together, and all the variables

4x-4

Back to the equation:

-(4x-4)


We get rid of parentheses

2x^2-12x-4x+4+2=0

We add all the numbers together, and all the variables

2x^2-16x+6=0

a = 2; b = -16; c = +6;
Δ = b2-4ac
Δ = -162-4·2·6
Δ = 208
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:

$\sqrt{\Delta}=\sqrt{208}=\sqrt{16*13}=\sqrt{16}*\sqrt{13}=4\sqrt{13}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-16)-4\sqrt{13}}{2*2}=\frac{16-4\sqrt{13}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-16)+4\sqrt{13}}{2*2}=\frac{16+4\sqrt{13}}{4}
$