x2-3x+6=65

Solution for x2-3x+6=65 equation:

x2-3x+6=65

We move all terms to the left:

x2-3x+6-(65)=0

We add all the numbers together, and all the variables

x^2-3x-59=0

a = 1; b = -3; c = -59;
Δ = b2-4ac
Δ = -32-4·1·(-59)
Δ = 245
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:

$\sqrt{\Delta}=\sqrt{245}=\sqrt{49*5}=\sqrt{49}*\sqrt{5}=7\sqrt{5}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3)-7\sqrt{5}}{2*1}=\frac{3-7\sqrt{5}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+7\sqrt{5}}{2*1}=\frac{3+7\sqrt{5}}{2}
$