2x^2-81x+693=0

Solution for 2x^2-81x+693=0 equation:

2x^2-81x+693=0

a = 2; b = -81; c = +693;
Δ = b2-4ac
Δ = -812-4·2·693
Δ = 1017
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{1017}=\sqrt{9*113}=\sqrt{9}*\sqrt{113}=3\sqrt{113}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-81)-3\sqrt{113}}{2*2}=\frac{81-3\sqrt{113}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-81)+3\sqrt{113}}{2*2}=\frac{81+3\sqrt{113}}{4}
$