a^2-32a+81=0

Solution for a^2-32a+81=0 equation:

a^2-32a+81=0

a = 1; b = -32; c = +81;
Δ = b2-4ac
Δ = -322-4·1·81
Δ = 700
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:

$\sqrt{\Delta}=\sqrt{700}=\sqrt{100*7}=\sqrt{100}*\sqrt{7}=10\sqrt{7}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-32)-10\sqrt{7}}{2*1}=\frac{32-10\sqrt{7}}{2}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-32)+10\sqrt{7}}{2*1}=\frac{32+10\sqrt{7}}{2}
$