2x^2-27x+65=0

Solution for 2x^2-27x+65=0 equation:

2x^2-27x+65=0

a = 2; b = -27; c = +65;
Δ = b2-4ac
Δ = -272-4·2·65
Δ = 209
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-27)-\sqrt{209}}{2*2}=\frac{27-\sqrt{209}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-27)+\sqrt{209}}{2*2}=\frac{27+\sqrt{209}}{4}
$