3/4k+9=6k=

Solution for 3/4k+9=6k= equation:

3/4k+9=6k=

We move all terms to the left:

3/4k+9-(6k)=0


Domain of the equation: 4k!=0

k!=0/4

k!=0

k∈R


We add all the numbers together, and all the variables

-6k+3/4k+9=0

We multiply all the terms by the denominator


-6k*4k+9*4k+3=0

Wy multiply elements

-24k^2+36k+3=0

a = -24; b = 36; c = +3;
Δ = b2-4ac
Δ = 362-4·(-24)·3
Δ = 1584
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:

$\sqrt{\Delta}=\sqrt{1584}=\sqrt{144*11}=\sqrt{144}*\sqrt{11}=12\sqrt{11}$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(36)-12\sqrt{11}}{2*-24}=\frac{-36-12\sqrt{11}}{-48}
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(36)+12\sqrt{11}}{2*-24}=\frac{-36+12\sqrt{11}}{-48}
$