2x^2-6x+9=19

Solution for 2x^2-6x+9=19 equation:

2x^2-6x+9=19

We move all terms to the left:

2x^2-6x+9-(19)=0

We add all the numbers together, and all the variables

2x^2-6x-10=0

a = 2; b = -6; c = -10;
Δ = b2-4ac
Δ = -62-4·2·(-10)
Δ = 116
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:

$\sqrt{\Delta}=\sqrt{116}=\sqrt{4*29}=\sqrt{4}*\sqrt{29}=2\sqrt{29}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-2\sqrt{29}}{2*2}=\frac{6-2\sqrt{29}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+2\sqrt{29}}{2*2}=\frac{6+2\sqrt{29}}{4}
$