2x^2+6x+9=65

Solution for 2x^2+6x+9=65 equation:

2x^2+6x+9=65

We move all terms to the left:

2x^2+6x+9-(65)=0

We add all the numbers together, and all the variables

2x^2+6x-56=0

a = 2; b = 6; c = -56;
Δ = b2-4ac
Δ = 62-4·2·(-56)
Δ = 484
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{484}=22$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-22}{2*2}=\frac{-28}{4}
=-7
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+22}{2*2}=\frac{16}{4}
=4
$