x^2+(-8)x-8=47

Solution for x^2+(-8)x-8=47 equation:

x^2+(-8)x-8=47

We move all terms to the left:

x^2+(-8)x-8-(47)=0

We add all the numbers together, and all the variables

x^2+(-8)x-55=0

We multiply parentheses

x^2-8x-55=0

a = 1; b = -8; c = -55;
Δ = b2-4ac
Δ = -82-4·1·(-55)
Δ = 284
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:

$\sqrt{\Delta}=\sqrt{284}=\sqrt{4*71}=\sqrt{4}*\sqrt{71}=2\sqrt{71}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-2\sqrt{71}}{2*1}=\frac{8-2\sqrt{71}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+2\sqrt{71}}{2*1}=\frac{8+2\sqrt{71}}{2}
$