x^2+30=24x

Solution for x^2+30=24x equation:

x^2+30=24x

We move all terms to the left:

x^2+30-(24x)=0

a = 1; b = -24; c = +30;
Δ = b2-4ac
Δ = -242-4·1·30
Δ = 456
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:

$\sqrt{\Delta}=\sqrt{456}=\sqrt{4*114}=\sqrt{4}*\sqrt{114}=2\sqrt{114}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-24)-2\sqrt{114}}{2*1}=\frac{24-2\sqrt{114}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-24)+2\sqrt{114}}{2*1}=\frac{24+2\sqrt{114}}{2}
$