X^2-14x+47=8

Solution for X^2-14x+47=8 equation:

X^2-14X+47=8

We move all terms to the left:

X^2-14X+47-(8)=0

We add all the numbers together, and all the variables

X^2-14X+39=0

a = 1; b = -14; c = +39;
Δ = b2-4ac
Δ = -142-4·1·39
Δ = 40
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:

$\sqrt{\Delta}=\sqrt{40}=\sqrt{4*10}=\sqrt{4}*\sqrt{10}=2\sqrt{10}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-14)-2\sqrt{10}}{2*1}=\frac{14-2\sqrt{10}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-14)+2\sqrt{10}}{2*1}=\frac{14+2\sqrt{10}}{2}
$