3a^2-96a+541=0

Solution for 3a^2-96a+541=0 equation:

3a^2-96a+541=0

a = 3; b = -96; c = +541;
Δ = b2-4ac
Δ = -962-4·3·541
Δ = 2724
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:

$\sqrt{\Delta}=\sqrt{2724}=\sqrt{4*681}=\sqrt{4}*\sqrt{681}=2\sqrt{681}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-96)-2\sqrt{681}}{2*3}=\frac{96-2\sqrt{681}}{6}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-96)+2\sqrt{681}}{2*3}=\frac{96+2\sqrt{681}}{6}
$