3(-1/4k+3)=1/4k

Solution for 3(-1/4k+3)=1/4k equation:

3(-1/4k+3)=1/4k

We move all terms to the left:

3(-1/4k+3)-(1/4k)=0


Domain of the equation: 4k+3)!=0

k∈R



Domain of the equation: 4k)!=0

k!=0/1

k!=0

k∈R


We add all the numbers together, and all the variables

3(-1/4k+3)-(+1/4k)=0

We multiply parentheses

-3k-(+1/4k)+9=0

We get rid of parentheses

-3k-1/4k+9=0

We multiply all the terms by the denominator


-3k*4k+9*4k-1=0

Wy multiply elements

-12k^2+36k-1=0

a = -12; b = 36; c = -1;
Δ = b2-4ac
Δ = 362-4·(-12)·(-1)
Δ = 1248
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:

$\sqrt{\Delta}=\sqrt{1248}=\sqrt{16*78}=\sqrt{16}*\sqrt{78}=4\sqrt{78}$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(36)-4\sqrt{78}}{2*-12}=\frac{-36-4\sqrt{78}}{-24}
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(36)+4\sqrt{78}}{2*-12}=\frac{-36+4\sqrt{78}}{-24}
$