5w(9-3w)=31

Solution for 5w(9-3w)=31 equation:

5w(9-3w)=31

We move all terms to the left:

5w(9-3w)-(31)=0

We add all the numbers together, and all the variables

5w(-3w+9)-31=0

We multiply parentheses

-15w^2+45w-31=0

a = -15; b = 45; c = -31;
Δ = b2-4ac
Δ = 452-4·(-15)·(-31)
Δ = 165
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(45)-\sqrt{165}}{2*-15}=\frac{-45-\sqrt{165}}{-30}
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(45)+\sqrt{165}}{2*-15}=\frac{-45+\sqrt{165}}{-30}
$