X^2-24x=-47

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

X^2-24X=-47

We move all terms to the left:

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

We add all the numbers together, and all the variables

X^2-24X+47=0

a = 1; b = -24; c = +47;
Δ = b2-4ac
Δ = -242-4·1·47
Δ = 388
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:

$\sqrt{\Delta}=\sqrt{388}=\sqrt{4*97}=\sqrt{4}*\sqrt{97}=2\sqrt{97}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-24)-2\sqrt{97}}{2*1}=\frac{24-2\sqrt{97}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-24)+2\sqrt{97}}{2*1}=\frac{24+2\sqrt{97}}{2}
$