3/10f-24=-1/5f

Solution for 3/10f-24=-1/5f equation:

3/10f-24=-1/5f

We move all terms to the left:

3/10f-24-(-1/5f)=0


Domain of the equation: 10f!=0

f!=0/10

f!=0

f∈R



Domain of the equation: 5f)!=0

f!=0/1

f!=0

f∈R


We get rid of parentheses

3/10f+1/5f-24=0

We calculate fractions


15f/50f^2+10f/50f^2-24=0

We multiply all the terms by the denominator


15f+10f-24*50f^2=0

We add all the numbers together, and all the variables

25f-24*50f^2=0

Wy multiply elements

-1200f^2+25f=0

a = -1200; b = 25; c = 0;
Δ = b2-4ac
Δ = 252-4·(-1200)·0
Δ = 625
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$f_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$f_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{625}=25$
$f_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(25)-25}{2*-1200}=\frac{-50}{-2400}
=1/48
$
$f_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(25)+25}{2*-1200}=\frac{0}{-2400}
=0
$