2/3f+4=3/5f-2

Solution for 2/3f+4=3/5f-2 equation:

2/3f+4=3/5f-2

We move all terms to the left:

2/3f+4-(3/5f-2)=0


Domain of the equation: 3f!=0

f!=0/3

f!=0

f∈R



Domain of the equation: 5f-2)!=0

f∈R


We get rid of parentheses

2/3f-3/5f+2+4=0

We calculate fractions


10f/15f^2+(-9f)/15f^2+2+4=0

We add all the numbers together, and all the variables

10f/15f^2+(-9f)/15f^2+6=0

We multiply all the terms by the denominator


10f+(-9f)+6*15f^2=0

Wy multiply elements

90f^2+10f+(-9f)=0

We get rid of parentheses

90f^2+10f-9f=0

We add all the numbers together, and all the variables

90f^2+f=0

a = 90; b = 1; c = 0;
Δ = b2-4ac
Δ = 12-4·90·0
Δ = 1
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$f_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$f_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1}=1$
$f_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-1}{2*90}=\frac{-2}{180}
=-1/90
$
$f_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+1}{2*90}=\frac{0}{180}
=0
$