e^2+1/4=3

Solution for e^2+1/4=3 equation:

e^2+1/4=3

We move all terms to the left:

e^2+1/4-(3)=0

determiningTheFunctionDomain
e^2-3+1/4=0

We multiply all the terms by the denominator


e^2*4+1-3*4=0

We add all the numbers together, and all the variables

e^2*4-11=0

Wy multiply elements

4e^2-11=0

a = 4; b = 0; c = -11;
Δ = b2-4ac
Δ = 02-4·4·(-11)
Δ = 176
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:

$\sqrt{\Delta}=\sqrt{176}=\sqrt{16*11}=\sqrt{16}*\sqrt{11}=4\sqrt{11}$
$e_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{11}}{2*4}=\frac{0-4\sqrt{11}}{8}
=-\frac{4\sqrt{11}}{8}
=-\frac{\sqrt{11}}{2}
$
$e_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{11}}{2*4}=\frac{0+4\sqrt{11}}{8}
=\frac{4\sqrt{11}}{8}
=\frac{\sqrt{11}}{2}
$