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

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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 $

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