7/15f-1/5f=10

Solution for 7/15f-1/5f=10 equation:

7/15f-1/5f=10

We move all terms to the left:

7/15f-1/5f-(10)=0


Domain of the equation: 15f!=0

f!=0/15

f!=0

f∈R



Domain of the equation: 5f!=0

f!=0/5

f!=0

f∈R


We calculate fractions


35f/75f^2+(-15f)/75f^2-10=0

We multiply all the terms by the denominator


35f+(-15f)-10*75f^2=0

Wy multiply elements

-750f^2+35f+(-15f)=0

We get rid of parentheses

-750f^2+35f-15f=0

We add all the numbers together, and all the variables

-750f^2+20f=0

a = -750; b = 20; c = 0;
Δ = b2-4ac
Δ = 202-4·(-750)·0
Δ = 400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$f_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$f_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{400}=20$
$f_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(20)-20}{2*-750}=\frac{-40}{-1500}
=2/75
$
$f_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(20)+20}{2*-750}=\frac{0}{-1500}
=0
$