10k-1=11/9k-43

Solution for 10k-1=11/9k-43 equation:

10k-1=11/9k-43

We move all terms to the left:

10k-1-(11/9k-43)=0


Domain of the equation: 9k-43)!=0

k∈R


We get rid of parentheses

10k-11/9k+43-1=0

We multiply all the terms by the denominator


10k*9k+43*9k-1*9k-11=0

Wy multiply elements

90k^2+387k-9k-11=0

We add all the numbers together, and all the variables

90k^2+378k-11=0

a = 90; b = 378; c = -11;
Δ = b2-4ac
Δ = 3782-4·90·(-11)
Δ = 146844
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{146844}=\sqrt{36*4079}=\sqrt{36}*\sqrt{4079}=6\sqrt{4079}$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(378)-6\sqrt{4079}}{2*90}=\frac{-378-6\sqrt{4079}}{180}
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(378)+6\sqrt{4079}}{2*90}=\frac{-378+6\sqrt{4079}}{180}
$