5/6e-53e=24

Solution for 5/6e-53e=24 equation:

5/6e-53e=24

We move all terms to the left:

5/6e-53e-(24)=0


Domain of the equation: 6e!=0

e!=0/6

e!=0

e∈R


We add all the numbers together, and all the variables

-53e+5/6e-24=0

We multiply all the terms by the denominator


-53e*6e-24*6e+5=0

Wy multiply elements

-318e^2-144e+5=0

a = -318; b = -144; c = +5;
Δ = b2-4ac
Δ = -1442-4·(-318)·5
Δ = 27096
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:

$\sqrt{\Delta}=\sqrt{27096}=\sqrt{4*6774}=\sqrt{4}*\sqrt{6774}=2\sqrt{6774}$
$e_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-144)-2\sqrt{6774}}{2*-318}=\frac{144-2\sqrt{6774}}{-636}
$
$e_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-144)+2\sqrt{6774}}{2*-318}=\frac{144+2\sqrt{6774}}{-636}
$