f(3/4)=11/2

Solution for f(3/4)=11/2 equation:

f(3/4)=11/2

We move all terms to the left:

f(3/4)-(11/2)=0

We add all the numbers together, and all the variables

f(+3/4)-(+11/2)=0

We multiply parentheses

3f^2-(+11/2)=0

We get rid of parentheses

3f^2-11/2=0

We multiply all the terms by the denominator


3f^2*2-11=0

Wy multiply elements

6f^2-11=0

a = 6; b = 0; c = -11;
Δ = b2-4ac
Δ = 02-4·6·(-11)
Δ = 264
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:

$\sqrt{\Delta}=\sqrt{264}=\sqrt{4*66}=\sqrt{4}*\sqrt{66}=2\sqrt{66}$
$f_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{66}}{2*6}=\frac{0-2\sqrt{66}}{12}
=-\frac{2\sqrt{66}}{12}
=-\frac{\sqrt{66}}{6}
$
$f_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{66}}{2*6}=\frac{0+2\sqrt{66}}{12}
=\frac{2\sqrt{66}}{12}
=\frac{\sqrt{66}}{6}
$