F(x)=9/3x-15

Solution for F(x)=9/3x-15 equation:

(F)=9/3F-15

We move all terms to the left:

(F)-(9/3F-15)=0


Domain of the equation: 3F-15)!=0

F∈R


We get rid of parentheses

F-9/3F+15=0

We multiply all the terms by the denominator


F*3F+15*3F-9=0

Wy multiply elements

3F^2+45F-9=0

a = 3; b = 45; c = -9;
Δ = b2-4ac
Δ = 452-4·3·(-9)
Δ = 2133
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:

$\sqrt{\Delta}=\sqrt{2133}=\sqrt{9*237}=\sqrt{9}*\sqrt{237}=3\sqrt{237}$
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(45)-3\sqrt{237}}{2*3}=\frac{-45-3\sqrt{237}}{6}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(45)+3\sqrt{237}}{2*3}=\frac{-45+3\sqrt{237}}{6}
$