2a^2-57a+81=0

Solution for 2a^2-57a+81=0 equation:

2a^2-57a+81=0

a = 2; b = -57; c = +81;
Δ = b2-4ac
Δ = -572-4·2·81
Δ = 2601
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2601}=51$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-57)-51}{2*2}=\frac{6}{4}
=1+1/2
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-57)+51}{2*2}=\frac{108}{4}
=27
$