6/7e=12e

Solution for 6/7e=12e equation:

6/7e=12e

We move all terms to the left:

6/7e-(12e)=0


Domain of the equation: 7e!=0

e!=0/7

e!=0

e∈R


We add all the numbers together, and all the variables

-12e+6/7e=0

We multiply all the terms by the denominator


-12e*7e+6=0

Wy multiply elements

-84e^2+6=0

a = -84; b = 0; c = +6;
Δ = b2-4ac
Δ = 02-4·(-84)·6
Δ = 2016
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:

$\sqrt{\Delta}=\sqrt{2016}=\sqrt{144*14}=\sqrt{144}*\sqrt{14}=12\sqrt{14}$
$e_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-12\sqrt{14}}{2*-84}=\frac{0-12\sqrt{14}}{-168}
=-\frac{12\sqrt{14}}{-168}
=-\frac{\sqrt{14}}{-14}
$
$e_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+12\sqrt{14}}{2*-84}=\frac{0+12\sqrt{14}}{-168}
=\frac{12\sqrt{14}}{-168}
=\frac{\sqrt{14}}{-14}
$