F(x)=7/3x-3

Solution for F(x)=7/3x-3 equation:

(F)=7/3F-3

We move all terms to the left:

(F)-(7/3F-3)=0


Domain of the equation: 3F-3)!=0

F∈R


We get rid of parentheses

F-7/3F+3=0

We multiply all the terms by the denominator


F*3F+3*3F-7=0

Wy multiply elements

3F^2+9F-7=0

a = 3; b = 9; c = -7;
Δ = b2-4ac
Δ = 92-4·3·(-7)
Δ = 165
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{-(9)-\sqrt{165}}{2*3}=\frac{-9-\sqrt{165}}{6}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+\sqrt{165}}{2*3}=\frac{-9+\sqrt{165}}{6}
$