1/4k+3+7+3k=-64

Solution for 1/4k+3+7+3k=-64 equation:

1/4k+3+7+3k=-64

We move all terms to the left:

1/4k+3+7+3k-(-64)=0


Domain of the equation: 4k!=0

k!=0/4

k!=0

k∈R


We add all the numbers together, and all the variables

3k+1/4k+74=0

We multiply all the terms by the denominator


3k*4k+74*4k+1=0

Wy multiply elements

12k^2+296k+1=0

a = 12; b = 296; c = +1;
Δ = b2-4ac
Δ = 2962-4·12·1
Δ = 87568
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:

$\sqrt{\Delta}=\sqrt{87568}=\sqrt{16*5473}=\sqrt{16}*\sqrt{5473}=4\sqrt{5473}$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(296)-4\sqrt{5473}}{2*12}=\frac{-296-4\sqrt{5473}}{24}
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(296)+4\sqrt{5473}}{2*12}=\frac{-296+4\sqrt{5473}}{24}
$