2u^2-27u+13=0

Solution for 2u^2-27u+13=0 equation:

2u^2-27u+13=0

a = 2; b = -27; c = +13;
Δ = b2-4ac
Δ = -272-4·2·13
Δ = 625
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$u_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$u_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{625}=25$
$u_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-27)-25}{2*2}=\frac{2}{4}
=1/2
$
$u_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-27)+25}{2*2}=\frac{52}{4}
=13
$