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

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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 $

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