w^2-w/3-310/3=0

Solution for w^2-w/3-310/3=0 equation:

w^2-w/3-310/3=0

We multiply all the terms by the denominator


w^2*3-w-310=0

We add all the numbers together, and all the variables

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

Wy multiply elements

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