x^2=24x+16

Solution for x^2=24x+16 equation:

x^2=24x+16

We move all terms to the left:

x^2-(24x+16)=0

We get rid of parentheses

x^2-24x-16=0

a = 1; b = -24; c = -16;
Δ = b2-4ac
Δ = -242-4·1·(-16)
Δ = 640
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:

$\sqrt{\Delta}=\sqrt{640}=\sqrt{64*10}=\sqrt{64}*\sqrt{10}=8\sqrt{10}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-24)-8\sqrt{10}}{2*1}=\frac{24-8\sqrt{10}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-24)+8\sqrt{10}}{2*1}=\frac{24+8\sqrt{10}}{2}
$