/9f-11=14f+4

Solution for /9f-11=14f+4 equation:

/9f-11=14f+4

We move all terms to the left:

/9f-11-(14f+4)=0


Domain of the equation: 9f!=0

f!=0/9

f!=0

f∈R


We get rid of parentheses

/9f-14f-4-11=0

We multiply all the terms by the denominator


-14f*9f-4*9f-11*9f+=0

We add all the numbers together, and all the variables

-14f*9f-4*9f-11*9f=0

Wy multiply elements

-126f^2-36f-99f=0

We add all the numbers together, and all the variables

-126f^2-135f=0

a = -126; b = -135; c = 0;
Δ = b2-4ac
Δ = -1352-4·(-126)·0
Δ = 18225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$f_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$f_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{18225}=135$
$f_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-135)-135}{2*-126}=\frac{0}{-252}
=0
$
$f_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-135)+135}{2*-126}=\frac{270}{-252}
=-1+1/14
$