f2=1/22+3

Solution for f2=1/22+3 equation:

f2=1/22+3

We move all terms to the left:

f2-(1/22+3)=0

We add all the numbers together, and all the variables

f^2-(1/22+3)=0

We get rid of parentheses

f^2-3-1/22=0

We multiply all the terms by the denominator


f^2*22-1-3*22=0

We add all the numbers together, and all the variables

f^2*22-67=0

Wy multiply elements

22f^2-67=0

a = 22; b = 0; c = -67;
Δ = b2-4ac
Δ = 02-4·22·(-67)
Δ = 5896
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$f_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$f_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{5896}=\sqrt{4*1474}=\sqrt{4}*\sqrt{1474}=2\sqrt{1474}$
$f_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{1474}}{2*22}=\frac{0-2\sqrt{1474}}{44}
=-\frac{2\sqrt{1474}}{44}
=-\frac{\sqrt{1474}}{22}
$
$f_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{1474}}{2*22}=\frac{0+2\sqrt{1474}}{44}
=\frac{2\sqrt{1474}}{44}
=\frac{\sqrt{1474}}{22}
$