5/3f+3=2f+2

Solution for 5/3f+3=2f+2 equation:

5/3f+3=2f+2

We move all terms to the left:

5/3f+3-(2f+2)=0


Domain of the equation: 3f!=0

f!=0/3

f!=0

f∈R


We get rid of parentheses

5/3f-2f-2+3=0

We multiply all the terms by the denominator


-2f*3f-2*3f+3*3f+5=0

Wy multiply elements

-6f^2-6f+9f+5=0

We add all the numbers together, and all the variables

-6f^2+3f+5=0

a = -6; b = 3; c = +5;
Δ = b2-4ac
Δ = 32-4·(-6)·5
Δ = 129
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{-(3)-\sqrt{129}}{2*-6}=\frac{-3-\sqrt{129}}{-12}
$
$f_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+\sqrt{129}}{2*-6}=\frac{-3+\sqrt{129}}{-12}
$