4w^2-94w+86=0

Solution for 4w^2-94w+86=0 equation:

4w^2-94w+86=0

a = 4; b = -94; c = +86;
Δ = b2-4ac
Δ = -942-4·4·86
Δ = 7460
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:

$\sqrt{\Delta}=\sqrt{7460}=\sqrt{4*1865}=\sqrt{4}*\sqrt{1865}=2\sqrt{1865}$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-94)-2\sqrt{1865}}{2*4}=\frac{94-2\sqrt{1865}}{8}
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-94)+2\sqrt{1865}}{2*4}=\frac{94+2\sqrt{1865}}{8}
$