F(x)=2/9x+4

Solution for F(x)=2/9x+4 equation:

(F)=2/9F+4

We move all terms to the left:

(F)-(2/9F+4)=0


Domain of the equation: 9F+4)!=0

F∈R


We get rid of parentheses

F-2/9F-4=0

We multiply all the terms by the denominator


F*9F-4*9F-2=0

Wy multiply elements

9F^2-36F-2=0

a = 9; b = -36; c = -2;
Δ = b2-4ac
Δ = -362-4·9·(-2)
Δ = 1368
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:

$\sqrt{\Delta}=\sqrt{1368}=\sqrt{36*38}=\sqrt{36}*\sqrt{38}=6\sqrt{38}$
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-36)-6\sqrt{38}}{2*9}=\frac{36-6\sqrt{38}}{18}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-36)+6\sqrt{38}}{2*9}=\frac{36+6\sqrt{38}}{18}
$