5/6e+10=-3+1/2e

Solution for 5/6e+10=-3+1/2e equation:

5/6e+10=-3+1/2e

We move all terms to the left:

5/6e+10-(-3+1/2e)=0


Domain of the equation: 6e!=0

e!=0/6

e!=0

e∈R



Domain of the equation: 2e)!=0

e!=0/1

e!=0

e∈R


We add all the numbers together, and all the variables

5/6e-(1/2e-3)+10=0

We get rid of parentheses

5/6e-1/2e+3+10=0

We calculate fractions


10e/12e^2+(-6e)/12e^2+3+10=0

We add all the numbers together, and all the variables

10e/12e^2+(-6e)/12e^2+13=0

We multiply all the terms by the denominator


10e+(-6e)+13*12e^2=0

Wy multiply elements

156e^2+10e+(-6e)=0

We get rid of parentheses

156e^2+10e-6e=0

We add all the numbers together, and all the variables

156e^2+4e=0

a = 156; b = 4; c = 0;
Δ = b2-4ac
Δ = 42-4·156·0
Δ = 16
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$e_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$e_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{16}=4$
$e_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-4}{2*156}=\frac{-8}{312}
=-1/39
$
$e_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+4}{2*156}=\frac{0}{312}
=0
$