2500=6w^2+4w

Solution for 2500=6w^2+4w equation:

2500=6w^2+4w

We move all terms to the left:

2500-(6w^2+4w)=0

We get rid of parentheses

-6w^2-4w+2500=0

a = -6; b = -4; c = +2500;
Δ = b2-4ac
Δ = -42-4·(-6)·2500
Δ = 60016
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:

$\sqrt{\Delta}=\sqrt{60016}=\sqrt{1936*31}=\sqrt{1936}*\sqrt{31}=44\sqrt{31}$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-44\sqrt{31}}{2*-6}=\frac{4-44\sqrt{31}}{-12}
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+44\sqrt{31}}{2*-6}=\frac{4+44\sqrt{31}}{-12}
$