f(-5)=-4(-5)-1/7

Solution for f(-5)=-4(-5)-1/7 equation:

f(-5)=-4(-5)-1/7

We move all terms to the left:

f(-5)-(-4(-5)-1/7)=0

We multiply parentheses

-5f-(-4(-5)-1/7)=0

We multiply all the terms by the denominator


-5f*7)-(-1-4(-5)=0

We add all the numbers together, and all the variables

-5f*7)-(+19=0

Wy multiply elements

-35f^2+19=0

a = -35; b = 0; c = +19;
Δ = b2-4ac
Δ = 02-4·(-35)·19
Δ = 2660
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:

$\sqrt{\Delta}=\sqrt{2660}=\sqrt{4*665}=\sqrt{4}*\sqrt{665}=2\sqrt{665}$
$f_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{665}}{2*-35}=\frac{0-2\sqrt{665}}{-70}
=-\frac{2\sqrt{665}}{-70}
=-\frac{\sqrt{665}}{-35}
$
$f_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{665}}{2*-35}=\frac{0+2\sqrt{665}}{-70}
=\frac{2\sqrt{665}}{-70}
=\frac{\sqrt{665}}{-35}
$