a*a+16a-256=0

Solution for a*a+16a-256=0 equation:

a*a+16a-256=0

We add all the numbers together, and all the variables

16a+a*a-256=0

Wy multiply elements

a^2+16a-256=0

a = 1; b = 16; c = -256;
Δ = b2-4ac
Δ = 162-4·1·(-256)
Δ = 1280
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{1280}=\sqrt{256*5}=\sqrt{256}*\sqrt{5}=16\sqrt{5}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(16)-16\sqrt{5}}{2*1}=\frac{-16-16\sqrt{5}}{2}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(16)+16\sqrt{5}}{2*1}=\frac{-16+16\sqrt{5}}{2}
$