F(x)=18/5x+3

Solution for F(x)=18/5x+3 equation:

(F)=18/5F+3

We move all terms to the left:

(F)-(18/5F+3)=0


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

F∈R


We get rid of parentheses

F-18/5F-3=0

We multiply all the terms by the denominator


F*5F-3*5F-18=0

Wy multiply elements

5F^2-15F-18=0

a = 5; b = -15; c = -18;
Δ = b2-4ac
Δ = -152-4·5·(-18)
Δ = 585
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:

$\sqrt{\Delta}=\sqrt{585}=\sqrt{9*65}=\sqrt{9}*\sqrt{65}=3\sqrt{65}$
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-15)-3\sqrt{65}}{2*5}=\frac{15-3\sqrt{65}}{10}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-15)+3\sqrt{65}}{2*5}=\frac{15+3\sqrt{65}}{10}
$