x2-14x+47=0

Solution for x2-14x+47=0 equation:

x2-14x+47=0

We add all the numbers together, and all the variables

x^2-14x+47=0

a = 1; b = -14; c = +47;
Δ = b2-4ac
Δ = -142-4·1·47
Δ = 8
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:

$\sqrt{\Delta}=\sqrt{8}=\sqrt{4*2}=\sqrt{4}*\sqrt{2}=2\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-14)-2\sqrt{2}}{2*1}=\frac{14-2\sqrt{2}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-14)+2\sqrt{2}}{2*1}=\frac{14+2\sqrt{2}}{2}
$