F/x=3x-4

Solution for F/x=3x-4 equation:

/F=3F-4

We move all terms to the left:

/F-(3F-4)=0


Domain of the equation: F!=0

F∈R


We get rid of parentheses

/F-3F+4=0

We multiply all the terms by the denominator


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

We add all the numbers together, and all the variables

4F-3F*F=0

Wy multiply elements

-3F^2+4F=0

a = -3; b = 4; c = 0;
Δ = b2-4ac
Δ = 42-4·(-3)·0
Δ = 16
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{16}=4$
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-4}{2*-3}=\frac{-8}{-6}
=1+1/3
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+4}{2*-3}=\frac{0}{-6}
=0
$