5/4e+3/10e=2

Solution for 5/4e+3/10e=2 equation:

5/4e+3/10e=2

We move all terms to the left:

5/4e+3/10e-(2)=0


Domain of the equation: 4e!=0

e!=0/4

e!=0

e∈R



Domain of the equation: 10e!=0

e!=0/10

e!=0

e∈R


We calculate fractions


50e/40e^2+12e/40e^2-2=0

We multiply all the terms by the denominator


50e+12e-2*40e^2=0

We add all the numbers together, and all the variables

62e-2*40e^2=0

Wy multiply elements

-80e^2+62e=0

a = -80; b = 62; c = 0;
Δ = b2-4ac
Δ = 622-4·(-80)·0
Δ = 3844
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$e_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$e_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{3844}=62$
$e_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(62)-62}{2*-80}=\frac{-124}{-160}
=31/40
$
$e_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(62)+62}{2*-80}=\frac{0}{-160}
=0
$