7e2+4=172

Solution for 7e2+4=172 equation:

7e^2+4=172

We move all terms to the left:

7e^2+4-(172)=0

We add all the numbers together, and all the variables

7e^2-168=0

a = 7; b = 0; c = -168;
Δ = b2-4ac
Δ = 02-4·7·(-168)
Δ = 4704
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:

$\sqrt{\Delta}=\sqrt{4704}=\sqrt{784*6}=\sqrt{784}*\sqrt{6}=28\sqrt{6}$
$e_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-28\sqrt{6}}{2*7}=\frac{0-28\sqrt{6}}{14}
=-\frac{28\sqrt{6}}{14}
=-2\sqrt{6}
$
$e_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+28\sqrt{6}}{2*7}=\frac{0+28\sqrt{6}}{14}
=\frac{28\sqrt{6}}{14}
=2\sqrt{6}
$