2w^2-88w+340=0

Solution for 2w^2-88w+340=0 equation:

2w^2-88w+340=0

a = 2; b = -88; c = +340;
Δ = b2-4ac
Δ = -882-4·2·340
Δ = 5024
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{5024}=\sqrt{16*314}=\sqrt{16}*\sqrt{314}=4\sqrt{314}$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-88)-4\sqrt{314}}{2*2}=\frac{88-4\sqrt{314}}{4}
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-88)+4\sqrt{314}}{2*2}=\frac{88+4\sqrt{314}}{4}
$