11/2*e=6

Solution for 11/2*e=6 equation:

11/2*e=6

We move all terms to the left:

11/2*e-(6)=0


Domain of the equation: 2*e!=0

e!=0/1

e!=0

e∈R


We multiply all the terms by the denominator


-6*2*e+11=0

Wy multiply elements

-12e*e+11=0

Wy multiply elements

-12e^2+11=0

a = -12; b = 0; c = +11;
Δ = b2-4ac
Δ = 02-4·(-12)·11
Δ = 528
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:

$\sqrt{\Delta}=\sqrt{528}=\sqrt{16*33}=\sqrt{16}*\sqrt{33}=4\sqrt{33}$
$e_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{33}}{2*-12}=\frac{0-4\sqrt{33}}{-24}
=-\frac{4\sqrt{33}}{-24}
=-\frac{\sqrt{33}}{-6}
$
$e_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{33}}{2*-12}=\frac{0+4\sqrt{33}}{-24}
=\frac{4\sqrt{33}}{-24}
=\frac{\sqrt{33}}{-6}
$