F(x)=10-9/2x

Solution for F(x)=10-9/2x equation:

(F)=10-9/2F

We move all terms to the left:

(F)-(10-9/2F)=0


Domain of the equation: 2F)!=0

F!=0/1

F!=0

F∈R


We add all the numbers together, and all the variables

F-(-9/2F+10)=0

We get rid of parentheses

F+9/2F-10=0

We multiply all the terms by the denominator


F*2F-10*2F+9=0

Wy multiply elements

2F^2-20F+9=0

a = 2; b = -20; c = +9;
Δ = b2-4ac
Δ = -202-4·2·9
Δ = 328
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:

$\sqrt{\Delta}=\sqrt{328}=\sqrt{4*82}=\sqrt{4}*\sqrt{82}=2\sqrt{82}$
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-20)-2\sqrt{82}}{2*2}=\frac{20-2\sqrt{82}}{4}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-20)+2\sqrt{82}}{2*2}=\frac{20+2\sqrt{82}}{4}
$