f(-5)=-2(-5)+1/3

Solution for f(-5)=-2(-5)+1/3 equation:

f(-5)=-2(-5)+1/3

We move all terms to the left:

f(-5)-(-2(-5)+1/3)=0

We multiply parentheses

-5f-(-2(-5)+1/3)=0

We multiply all the terms by the denominator


-5f*3)-(+1-2(-5)=0

We add all the numbers together, and all the variables

-5f*3)-(+11=0

Wy multiply elements

-15f^2+11=0

a = -15; b = 0; c = +11;
Δ = b2-4ac
Δ = 02-4·(-15)·11
Δ = 660
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:

$\sqrt{\Delta}=\sqrt{660}=\sqrt{4*165}=\sqrt{4}*\sqrt{165}=2\sqrt{165}$
$f_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{165}}{2*-15}=\frac{0-2\sqrt{165}}{-30}
=-\frac{2\sqrt{165}}{-30}
=-\frac{\sqrt{165}}{-15}
$
$f_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{165}}{2*-15}=\frac{0+2\sqrt{165}}{-30}
=\frac{2\sqrt{165}}{-30}
=\frac{\sqrt{165}}{-15}
$