7/5f+9/10+1/10f=5/8

Solution for 7/5f+9/10+1/10f=5/8 equation:

7/5f+9/10+1/10f=5/8

We move all terms to the left:

7/5f+9/10+1/10f-(5/8)=0


Domain of the equation: 5f!=0

f!=0/5

f!=0

f∈R



Domain of the equation: 10f!=0

f!=0/10

f!=0

f∈R


We add all the numbers together, and all the variables

7/5f+1/10f+9/10-(+5/8)=0

We get rid of parentheses

7/5f+1/10f+9/10-5/8=0

We calculate fractions


(-2500f^2)/4000f^2+5600f/4000f^2+320f/4000f^2+2880f/4000f^2=0

We multiply all the terms by the denominator


(-2500f^2)+5600f+320f+2880f=0

We add all the numbers together, and all the variables

(-2500f^2)+8800f=0

We get rid of parentheses

-2500f^2+8800f=0

a = -2500; b = 8800; c = 0;
Δ = b2-4ac
Δ = 88002-4·(-2500)·0
Δ = 77440000
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$f_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$f_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{77440000}=8800$
$f_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8800)-8800}{2*-2500}=\frac{-17600}{-5000}
=3+13/25
$
$f_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8800)+8800}{2*-2500}=\frac{0}{-5000}
=0
$