x2-14x+53=9

Solution for x2-14x+53=9 equation:

x2-14x+53=9

We move all terms to the left:

x2-14x+53-(9)=0

We add all the numbers together, and all the variables

x^2-14x+44=0

a = 1; b = -14; c = +44;
Δ = b2-4ac
Δ = -142-4·1·44
Δ = 20
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:

$\sqrt{\Delta}=\sqrt{20}=\sqrt{4*5}=\sqrt{4}*\sqrt{5}=2\sqrt{5}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-14)-2\sqrt{5}}{2*1}=\frac{14-2\sqrt{5}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-14)+2\sqrt{5}}{2*1}=\frac{14+2\sqrt{5}}{2}
$