F(x)=5/9x-2

Solution for F(x)=5/9x-2 equation:

(F)=5/9F-2

We move all terms to the left:

(F)-(5/9F-2)=0


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

F∈R


We get rid of parentheses

F-5/9F+2=0

We multiply all the terms by the denominator


F*9F+2*9F-5=0

Wy multiply elements

9F^2+18F-5=0

a = 9; b = 18; c = -5;
Δ = b2-4ac
Δ = 182-4·9·(-5)
Δ = 504
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:

$\sqrt{\Delta}=\sqrt{504}=\sqrt{36*14}=\sqrt{36}*\sqrt{14}=6\sqrt{14}$
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(18)-6\sqrt{14}}{2*9}=\frac{-18-6\sqrt{14}}{18}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(18)+6\sqrt{14}}{2*9}=\frac{-18+6\sqrt{14}}{18}
$