2-3/4f=1/8f-9

Solution for 2-3/4f=1/8f-9 equation:

2-3/4f=1/8f-9

We move all terms to the left:

2-3/4f-(1/8f-9)=0


Domain of the equation: 4f!=0

f!=0/4

f!=0

f∈R



Domain of the equation: 8f-9)!=0

f∈R


We get rid of parentheses

-3/4f-1/8f+9+2=0

We calculate fractions


(-24f)/32f^2+(-4f)/32f^2+9+2=0

We add all the numbers together, and all the variables

(-24f)/32f^2+(-4f)/32f^2+11=0

We multiply all the terms by the denominator


(-24f)+(-4f)+11*32f^2=0

Wy multiply elements

352f^2+(-24f)+(-4f)=0

We get rid of parentheses

352f^2-24f-4f=0

We add all the numbers together, and all the variables

352f^2-28f=0

a = 352; b = -28; c = 0;
Δ = b2-4ac
Δ = -282-4·352·0
Δ = 784
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$f_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$f_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{784}=28$
$f_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-28)-28}{2*352}=\frac{0}{704}
=0
$
$f_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-28)+28}{2*352}=\frac{56}{704}
=7/88
$