2(x2-6x+9)-8(x-3)+6=0

Solution for 2(x2-6x+9)-8(x-3)+6=0 equation:

2(x2-6x+9)-8(x-3)+6=0

We add all the numbers together, and all the variables

2(+x^2-6x+9)-8(x-3)+6=0

We multiply parentheses

2x^2-12x-8x+18+24+6=0

We add all the numbers together, and all the variables

2x^2-20x+48=0

a = 2; b = -20; c = +48;
Δ = b2-4ac
Δ = -202-4·2·48
Δ = 16
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{16}=4$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-20)-4}{2*2}=\frac{16}{4}
=4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-20)+4}{2*2}=\frac{24}{4}
=6
$