9x^2-2x+3=65

Solution for 9x^2-2x+3=65 equation:

9x^2-2x+3=65

We move all terms to the left:

9x^2-2x+3-(65)=0

We add all the numbers together, and all the variables

9x^2-2x-62=0

a = 9; b = -2; c = -62;
Δ = b2-4ac
Δ = -22-4·9·(-62)
Δ = 2236
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:

$\sqrt{\Delta}=\sqrt{2236}=\sqrt{4*559}=\sqrt{4}*\sqrt{559}=2\sqrt{559}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-2\sqrt{559}}{2*9}=\frac{2-2\sqrt{559}}{18}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+2\sqrt{559}}{2*9}=\frac{2+2\sqrt{559}}{18}
$