f(-5)=-6(-5)-2/3

Solution for f(-5)=-6(-5)-2/3 equation:

f(-5)=-6(-5)-2/3

We move all terms to the left:

f(-5)-(-6(-5)-2/3)=0

We multiply parentheses

-5f-(-6(-5)-2/3)=0

We multiply all the terms by the denominator


-5f*3)-(-2-6(-5)=0

We add all the numbers together, and all the variables

-5f*3)-(+28=0

Wy multiply elements

-15f^2+28=0

a = -15; b = 0; c = +28;
Δ = b2-4ac
Δ = 02-4·(-15)·28
Δ = 1680
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:

$\sqrt{\Delta}=\sqrt{1680}=\sqrt{16*105}=\sqrt{16}*\sqrt{105}=4\sqrt{105}$
$f_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{105}}{2*-15}=\frac{0-4\sqrt{105}}{-30}
=-\frac{4\sqrt{105}}{-30}
=-\frac{2\sqrt{105}}{-15}
$
$f_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{105}}{2*-15}=\frac{0+4\sqrt{105}}{-30}
=\frac{4\sqrt{105}}{-30}
=\frac{2\sqrt{105}}{-15}
$