2x^2+62=24x

Solution for 2x^2+62=24x equation:

2x^2+62=24x

We move all terms to the left:

2x^2+62-(24x)=0

a = 2; b = -24; c = +62;
Δ = b2-4ac
Δ = -242-4·2·62
Δ = 80
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:

$\sqrt{\Delta}=\sqrt{80}=\sqrt{16*5}=\sqrt{16}*\sqrt{5}=4\sqrt{5}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-24)-4\sqrt{5}}{2*2}=\frac{24-4\sqrt{5}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-24)+4\sqrt{5}}{2*2}=\frac{24+4\sqrt{5}}{4}
$