2w^2-24=600

Solution for 2w^2-24=600 equation:

2w^2-24=600

We move all terms to the left:

2w^2-24-(600)=0

We add all the numbers together, and all the variables

2w^2-624=0

a = 2; b = 0; c = -624;
Δ = b2-4ac
Δ = 02-4·2·(-624)
Δ = 4992
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:

$\sqrt{\Delta}=\sqrt{4992}=\sqrt{64*78}=\sqrt{64}*\sqrt{78}=8\sqrt{78}$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-8\sqrt{78}}{2*2}=\frac{0-8\sqrt{78}}{4}
=-\frac{8\sqrt{78}}{4}
=-2\sqrt{78}
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+8\sqrt{78}}{2*2}=\frac{0+8\sqrt{78}}{4}
=\frac{8\sqrt{78}}{4}
=2\sqrt{78}
$