F(x)=-1/5x-2

Solution for F(x)=-1/5x-2 equation:

(F)=-1/5F-2

We move all terms to the left:

(F)-(-1/5F-2)=0


Domain of the equation: 5F-2)!=0

F∈R


We get rid of parentheses

F+1/5F+2=0

We multiply all the terms by the denominator


F*5F+2*5F+1=0

Wy multiply elements

5F^2+10F+1=0

a = 5; b = 10; c = +1;
Δ = b2-4ac
Δ = 102-4·5·1
Δ = 80
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:

$\sqrt{\Delta}=\sqrt{80}=\sqrt{16*5}=\sqrt{16}*\sqrt{5}=4\sqrt{5}$
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-4\sqrt{5}}{2*5}=\frac{-10-4\sqrt{5}}{10}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+4\sqrt{5}}{2*5}=\frac{-10+4\sqrt{5}}{10}
$