7e^2-2=12

Solution for 7e^2-2=12 equation:

7e^2-2=12

We move all terms to the left:

7e^2-2-(12)=0

We add all the numbers together, and all the variables

7e^2-14=0

a = 7; b = 0; c = -14;
Δ = b2-4ac
Δ = 02-4·7·(-14)
Δ = 392
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:

$\sqrt{\Delta}=\sqrt{392}=\sqrt{196*2}=\sqrt{196}*\sqrt{2}=14\sqrt{2}$
$e_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-14\sqrt{2}}{2*7}=\frac{0-14\sqrt{2}}{14}
=-\frac{14\sqrt{2}}{14}
=-\sqrt{2}
$
$e_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+14\sqrt{2}}{2*7}=\frac{0+14\sqrt{2}}{14}
=\frac{14\sqrt{2}}{14}
=\sqrt{2}
$