1/22*e=25

Solution for 1/22*e=25 equation:

1/22*e=25

We move all terms to the left:

1/22*e-(25)=0


Domain of the equation: 22*e!=0

e!=0/1

e!=0

e∈R


We multiply all the terms by the denominator


-25*22*e+1=0

Wy multiply elements

-550e*e+1=0

Wy multiply elements

-550e^2+1=0

a = -550; b = 0; c = +1;
Δ = b2-4ac
Δ = 02-4·(-550)·1
Δ = 2200
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:

$\sqrt{\Delta}=\sqrt{2200}=\sqrt{100*22}=\sqrt{100}*\sqrt{22}=10\sqrt{22}$
$e_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-10\sqrt{22}}{2*-550}=\frac{0-10\sqrt{22}}{-1100}
=-\frac{10\sqrt{22}}{-1100}
=-\frac{\sqrt{22}}{-110}
$
$e_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+10\sqrt{22}}{2*-550}=\frac{0+10\sqrt{22}}{-1100}
=\frac{10\sqrt{22}}{-1100}
=\frac{\sqrt{22}}{-110}
$