F(x)=-1/5x+3

Solution for F(x)=-1/5x+3 equation:

(F)=-1/5F+3

We move all terms to the left:

(F)-(-1/5F+3)=0


Domain of the equation: 5F+3)!=0

F∈R


We get rid of parentheses

F+1/5F-3=0

We multiply all the terms by the denominator


F*5F-3*5F+1=0

Wy multiply elements

5F^2-15F+1=0

a = 5; b = -15; c = +1;
Δ = b2-4ac
Δ = -152-4·5·1
Δ = 205
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-15)-\sqrt{205}}{2*5}=\frac{15-\sqrt{205}}{10}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-15)+\sqrt{205}}{2*5}=\frac{15+\sqrt{205}}{10}
$