F(x)=15/2x-9

Solution for F(x)=15/2x-9 equation:

(F)=15/2F-9

We move all terms to the left:

(F)-(15/2F-9)=0


Domain of the equation: 2F-9)!=0

F∈R


We get rid of parentheses

F-15/2F+9=0

We multiply all the terms by the denominator


F*2F+9*2F-15=0

Wy multiply elements

2F^2+18F-15=0

a = 2; b = 18; c = -15;
Δ = b2-4ac
Δ = 182-4·2·(-15)
Δ = 444
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:

$\sqrt{\Delta}=\sqrt{444}=\sqrt{4*111}=\sqrt{4}*\sqrt{111}=2\sqrt{111}$
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(18)-2\sqrt{111}}{2*2}=\frac{-18-2\sqrt{111}}{4}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(18)+2\sqrt{111}}{2*2}=\frac{-18+2\sqrt{111}}{4}
$