1/2e-3=3/4e+11

Solution for 1/2e-3=3/4e+11 equation:

1/2e-3=3/4e+11

We move all terms to the left:

1/2e-3-(3/4e+11)=0


Domain of the equation: 2e!=0

e!=0/2

e!=0

e∈R



Domain of the equation: 4e+11)!=0

e∈R


We get rid of parentheses

1/2e-3/4e-11-3=0

We calculate fractions


4e/8e^2+(-6e)/8e^2-11-3=0

We add all the numbers together, and all the variables

4e/8e^2+(-6e)/8e^2-14=0

We multiply all the terms by the denominator


4e+(-6e)-14*8e^2=0

Wy multiply elements

-112e^2+4e+(-6e)=0

We get rid of parentheses

-112e^2+4e-6e=0

We add all the numbers together, and all the variables

-112e^2-2e=0

a = -112; b = -2; c = 0;
Δ = b2-4ac
Δ = -22-4·(-112)·0
Δ = 4
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$e_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$e_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4}=2$
$e_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-2}{2*-112}=\frac{0}{-224}
=0
$
$e_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+2}{2*-112}=\frac{4}{-224}
=-1/56
$