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

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}
$