7/9k-4=4k+8

Solution for 7/9k-4=4k+8 equation:

7/9k-4=4k+8

We move all terms to the left:

7/9k-4-(4k+8)=0


Domain of the equation: 9k!=0

k!=0/9

k!=0

k∈R


We get rid of parentheses

7/9k-4k-8-4=0

We multiply all the terms by the denominator


-4k*9k-8*9k-4*9k+7=0

Wy multiply elements

-36k^2-72k-36k+7=0

We add all the numbers together, and all the variables

-36k^2-108k+7=0

a = -36; b = -108; c = +7;
Δ = b2-4ac
Δ = -1082-4·(-36)·7
Δ = 12672
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:

$\sqrt{\Delta}=\sqrt{12672}=\sqrt{576*22}=\sqrt{576}*\sqrt{22}=24\sqrt{22}$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-108)-24\sqrt{22}}{2*-36}=\frac{108-24\sqrt{22}}{-72}
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-108)+24\sqrt{22}}{2*-36}=\frac{108+24\sqrt{22}}{-72}
$