2x2-12x+18=64

Solution for 2x2-12x+18=64 equation:

2x^2-12x+18=64

We move all terms to the left:

2x^2-12x+18-(64)=0

We add all the numbers together, and all the variables

2x^2-12x-46=0

a = 2; b = -12; c = -46;
Δ = b2-4ac
Δ = -122-4·2·(-46)
Δ = 512
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:

$\sqrt{\Delta}=\sqrt{512}=\sqrt{256*2}=\sqrt{256}*\sqrt{2}=16\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-16\sqrt{2}}{2*2}=\frac{12-16\sqrt{2}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+16\sqrt{2}}{2*2}=\frac{12+16\sqrt{2}}{4}
$