9a^2-160a-256=0

Solution for 9a^2-160a-256=0 equation:

9a^2-160a-256=0

a = 9; b = -160; c = -256;
Δ = b2-4ac
Δ = -1602-4·9·(-256)
Δ = 34816
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:

$\sqrt{\Delta}=\sqrt{34816}=\sqrt{1024*34}=\sqrt{1024}*\sqrt{34}=32\sqrt{34}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-160)-32\sqrt{34}}{2*9}=\frac{160-32\sqrt{34}}{18}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-160)+32\sqrt{34}}{2*9}=\frac{160+32\sqrt{34}}{18}
$