F(x)=40-4/3x

Solution for F(x)=40-4/3x equation:

(F)=40-4/3F

We move all terms to the left:

(F)-(40-4/3F)=0


Domain of the equation: 3F)!=0

F!=0/1

F!=0

F∈R


We add all the numbers together, and all the variables

F-(-4/3F+40)=0

We get rid of parentheses

F+4/3F-40=0

We multiply all the terms by the denominator


F*3F-40*3F+4=0

Wy multiply elements

3F^2-120F+4=0

a = 3; b = -120; c = +4;
Δ = b2-4ac
Δ = -1202-4·3·4
Δ = 14352
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:

$\sqrt{\Delta}=\sqrt{14352}=\sqrt{16*897}=\sqrt{16}*\sqrt{897}=4\sqrt{897}$
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-120)-4\sqrt{897}}{2*3}=\frac{120-4\sqrt{897}}{6}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-120)+4\sqrt{897}}{2*3}=\frac{120+4\sqrt{897}}{6}
$