2x(x-8)+4=6(x-2)-4

Solution for 2x(x-8)+4=6(x-2)-4 equation:

2x(x-8)+4=6(x-2)-4

We move all terms to the left:

2x(x-8)+4-(6(x-2)-4)=0

We multiply parentheses

2x^2-16x-(6(x-2)-4)+4=0


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

6(x-2)-4

We multiply parentheses

6x-12-4

We add all the numbers together, and all the variables

6x-16

Back to the equation:

-(6x-16)


We get rid of parentheses

2x^2-16x-6x+16+4=0

We add all the numbers together, and all the variables

2x^2-22x+20=0

a = 2; b = -22; c = +20;
Δ = b2-4ac
Δ = -222-4·2·20
Δ = 324
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{324}=18$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-22)-18}{2*2}=\frac{4}{4}
=1
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-22)+18}{2*2}=\frac{40}{4}
=10
$