x^2-14x+3=9

Solution for x^2-14x+3=9 equation:

x^2-14x+3=9

We move all terms to the left:

x^2-14x+3-(9)=0

We add all the numbers together, and all the variables

x^2-14x-6=0

a = 1; b = -14; c = -6;
Δ = b2-4ac
Δ = -142-4·1·(-6)
Δ = 220
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:

$\sqrt{\Delta}=\sqrt{220}=\sqrt{4*55}=\sqrt{4}*\sqrt{55}=2\sqrt{55}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-14)-2\sqrt{55}}{2*1}=\frac{14-2\sqrt{55}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-14)+2\sqrt{55}}{2*1}=\frac{14+2\sqrt{55}}{2}
$