X2-24x=30

Solution for X2-24x=30 equation:

X2-24X=30

We move all terms to the left:

X2-24X-(30)=0

We add all the numbers together, and all the variables

X^2-24X-30=0

a = 1; b = -24; c = -30;
Δ = b2-4ac
Δ = -242-4·1·(-30)
Δ = 696
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:

$\sqrt{\Delta}=\sqrt{696}=\sqrt{4*174}=\sqrt{4}*\sqrt{174}=2\sqrt{174}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-24)-2\sqrt{174}}{2*1}=\frac{24-2\sqrt{174}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-24)+2\sqrt{174}}{2*1}=\frac{24+2\sqrt{174}}{2}
$