k/15k-9k+44=110

Solution for k/15k-9k+44=110 equation:

k/15k-9k+44=110

We move all terms to the left:

k/15k-9k+44-(110)=0


Domain of the equation: 15k!=0

k!=0/15

k!=0

k∈R


We add all the numbers together, and all the variables

-9k+k/15k-66=0

We multiply all the terms by the denominator


-9k*15k+k-66*15k=0

We add all the numbers together, and all the variables

k-9k*15k-66*15k=0

Wy multiply elements

-135k^2+k-990k=0

We add all the numbers together, and all the variables

-135k^2-989k=0

a = -135; b = -989; c = 0;
Δ = b2-4ac
Δ = -9892-4·(-135)·0
Δ = 978121
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{978121}=989$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-989)-989}{2*-135}=\frac{0}{-270}
=0
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-989)+989}{2*-135}=\frac{1978}{-270}
=-7+44/135
$