11/2*e=8

Solution for 11/2*e=8 equation:

11/2*e=8

We move all terms to the left:

11/2*e-(8)=0


Domain of the equation: 2*e!=0

e!=0/1

e!=0

e∈R


We multiply all the terms by the denominator


-8*2*e+11=0

Wy multiply elements

-16e*e+11=0

Wy multiply elements

-16e^2+11=0

a = -16; b = 0; c = +11;
Δ = b2-4ac
Δ = 02-4·(-16)·11
Δ = 704
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:

$\sqrt{\Delta}=\sqrt{704}=\sqrt{64*11}=\sqrt{64}*\sqrt{11}=8\sqrt{11}$
$e_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-8\sqrt{11}}{2*-16}=\frac{0-8\sqrt{11}}{-32}
=-\frac{8\sqrt{11}}{-32}
=-\frac{\sqrt{11}}{-4}
$
$e_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+8\sqrt{11}}{2*-16}=\frac{0+8\sqrt{11}}{-32}
=\frac{8\sqrt{11}}{-32}
=\frac{\sqrt{11}}{-4}
$