7e(2e-1)-3=6+6e

Solution for 7e(2e-1)-3=6+6e equation:

7e(2e-1)-3=6+6e

We move all terms to the left:

7e(2e-1)-3-(6+6e)=0

We add all the numbers together, and all the variables

7e(2e-1)-(6e+6)-3=0

We multiply parentheses

14e^2-7e-(6e+6)-3=0

We get rid of parentheses

14e^2-7e-6e-6-3=0

We add all the numbers together, and all the variables

14e^2-13e-9=0

a = 14; b = -13; c = -9;
Δ = b2-4ac
Δ = -132-4·14·(-9)
Δ = 673
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$e_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$e_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$e_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-13)-\sqrt{673}}{2*14}=\frac{13-\sqrt{673}}{28}
$
$e_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-13)+\sqrt{673}}{2*14}=\frac{13+\sqrt{673}}{28}
$