6000=40w^2+40w^2

Solution for 6000=40w^2+40w^2 equation:

6000=40w^2+40w^2

We move all terms to the left:

6000-(40w^2+40w^2)=0

We get rid of parentheses

-40w^2-40w^2+6000=0

We add all the numbers together, and all the variables

-80w^2+6000=0

a = -80; b = 0; c = +6000;
Δ = b2-4ac
Δ = 02-4·(-80)·6000
Δ = 1920000
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:

$\sqrt{\Delta}=\sqrt{1920000}=\sqrt{640000*3}=\sqrt{640000}*\sqrt{3}=800\sqrt{3}$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-800\sqrt{3}}{2*-80}=\frac{0-800\sqrt{3}}{-160}
=-\frac{800\sqrt{3}}{-160}
=-\frac{5\sqrt{3}}{-1}
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+800\sqrt{3}}{2*-80}=\frac{0+800\sqrt{3}}{-160}
=\frac{800\sqrt{3}}{-160}
=\frac{5\sqrt{3}}{-1}
$