-5w^2+31w-30=0

Solution for -5w^2+31w-30=0 equation:

-5w^2+31w-30=0

a = -5; b = 31; c = -30;
Δ = b2-4ac
Δ = 312-4·(-5)·(-30)
Δ = 361
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{361}=19$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(31)-19}{2*-5}=\frac{-50}{-10}
=+5
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(31)+19}{2*-5}=\frac{-12}{-10}
=1+1/5
$