X^2-24x+47=-8x

Solution for X^2-24x+47=-8x equation:

X^2-24X+47=-8X

We move all terms to the left:

X^2-24X+47-(-8X)=0

We get rid of parentheses

X^2-24X+8X+47=0

We add all the numbers together, and all the variables

X^2-16X+47=0

a = 1; b = -16; c = +47;
Δ = b2-4ac
Δ = -162-4·1·47
Δ = 68
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:

$\sqrt{\Delta}=\sqrt{68}=\sqrt{4*17}=\sqrt{4}*\sqrt{17}=2\sqrt{17}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-16)-2\sqrt{17}}{2*1}=\frac{16-2\sqrt{17}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-16)+2\sqrt{17}}{2*1}=\frac{16+2\sqrt{17}}{2}
$