12e^2=200

Solution for 12e^2=200 equation:

12e^2=200

We move all terms to the left:

12e^2-(200)=0

a = 12; b = 0; c = -200;
Δ = b2-4ac
Δ = 02-4·12·(-200)
Δ = 9600
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$e_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$e_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{9600}=\sqrt{1600*6}=\sqrt{1600}*\sqrt{6}=40\sqrt{6}$
$e_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-40\sqrt{6}}{2*12}=\frac{0-40\sqrt{6}}{24}
=-\frac{40\sqrt{6}}{24}
=-\frac{5\sqrt{6}}{3}
$
$e_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+40\sqrt{6}}{2*12}=\frac{0+40\sqrt{6}}{24}
=\frac{40\sqrt{6}}{24}
=\frac{5\sqrt{6}}{3}
$