F(x)=5-4/3x

Solution for F(x)=5-4/3x equation:

(F)=5-4/3F

We move all terms to the left:

(F)-(5-4/3F)=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+5)=0

We get rid of parentheses

F+4/3F-5=0

We multiply all the terms by the denominator


F*3F-5*3F+4=0

Wy multiply elements

3F^2-15F+4=0

a = 3; b = -15; c = +4;
Δ = b2-4ac
Δ = -152-4·3·4
Δ = 177
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-15)-\sqrt{177}}{2*3}=\frac{15-\sqrt{177}}{6}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-15)+\sqrt{177}}{2*3}=\frac{15+\sqrt{177}}{6}
$