2x^2-6x+9=17

Solution for 2x^2-6x+9=17 equation:

2x^2-6x+9=17

We move all terms to the left:

2x^2-6x+9-(17)=0

We add all the numbers together, and all the variables

2x^2-6x-8=0

a = 2; b = -6; c = -8;
Δ = b2-4ac
Δ = -62-4·2·(-8)
Δ = 100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{100}=10$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-10}{2*2}=\frac{-4}{4}
=-1
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+10}{2*2}=\frac{16}{4}
=4
$