310=(3w-1)w

Solution for 310=(3w-1)w equation:

310=(3w-1)w

We move all terms to the left:

310-((3w-1)w)=0


We calculate terms in parentheses: -((3w-1)w), so:

(3w-1)w

We multiply parentheses

3w^2-1w

Back to the equation:

-(3w^2-1w)


We get rid of parentheses

-3w^2+1w+310=0

We add all the numbers together, and all the variables

-3w^2+w+310=0

a = -3; b = 1; c = +310;
Δ = b2-4ac
Δ = 12-4·(-3)·310
Δ = 3721
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{3721}=61$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-61}{2*-3}=\frac{-62}{-6}
=10+1/3
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+61}{2*-3}=\frac{60}{-6}
=-10
$