2w2-23w+11=0

Solution for 2w2-23w+11=0 equation:

2w^2-23w+11=0

a = 2; b = -23; c = +11;
Δ = b2-4ac
Δ = -232-4·2·11
Δ = 441
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{441}=21$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-23)-21}{2*2}=\frac{2}{4}
=1/2
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-23)+21}{2*2}=\frac{44}{4}
=11
$