(14/9)k+11/9-2k+2/9+(2/9)k-5=0

Solution for (14/9)k+11/9-2k+2/9+(2/9)k-5=0 equation:

(14/9)k+11/9-2k+2/9+(2/9)k-5=0


Domain of the equation: 9)k!=0

k!=0/1

k!=0

k∈R


We add all the numbers together, and all the variables

(+14/9)k-2k+(+2/9)k-5+11/9+2/9=0

We add all the numbers together, and all the variables

-2k+(+14/9)k+(+2/9)k-5+11/9+2/9=0

We multiply parentheses

14k^2+2k^2-2k-5+11/9+2/9=0

We multiply all the terms by the denominator


14k^2*9+2k^2*9-2k*9+11+2-5*9=0

We add all the numbers together, and all the variables

14k^2*9+2k^2*9-2k*9-32=0

Wy multiply elements

126k^2+18k^2-18k-32=0

We add all the numbers together, and all the variables

144k^2-18k-32=0

a = 144; b = -18; c = -32;
Δ = b2-4ac
Δ = -182-4·144·(-32)
Δ = 18756
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:

$\sqrt{\Delta}=\sqrt{18756}=\sqrt{36*521}=\sqrt{36}*\sqrt{521}=6\sqrt{521}$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-18)-6\sqrt{521}}{2*144}=\frac{18-6\sqrt{521}}{288}
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-18)+6\sqrt{521}}{2*144}=\frac{18+6\sqrt{521}}{288}
$