7/8f+8/5f-9/5=12

Solution for 7/8f+8/5f-9/5=12 equation:

7/8f+8/5f-9/5=12

We move all terms to the left:

7/8f+8/5f-9/5-(12)=0


Domain of the equation: 8f!=0

f!=0/8

f!=0

f∈R



Domain of the equation: 5f!=0

f!=0/5

f!=0

f∈R


determiningTheFunctionDomain
7/8f+8/5f-12-9/5=0

We calculate fractions


875f/1000f^2+64f/1000f^2+(-72f)/1000f^2-12=0

We multiply all the terms by the denominator


875f+64f+(-72f)-12*1000f^2=0

We add all the numbers together, and all the variables

939f+(-72f)-12*1000f^2=0

Wy multiply elements

-12000f^2+939f+(-72f)=0

We get rid of parentheses

-12000f^2+939f-72f=0

We add all the numbers together, and all the variables

-12000f^2+867f=0

a = -12000; b = 867; c = 0;
Δ = b2-4ac
Δ = 8672-4·(-12000)·0
Δ = 751689
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$f_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$f_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{751689}=867$
$f_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(867)-867}{2*-12000}=\frac{-1734}{-24000}
=289/4000
$
$f_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(867)+867}{2*-12000}=\frac{0}{-24000}
=0
$