-1/4k-9/4=-4-1/2k

Solution for -1/4k-9/4=-4-1/2k equation:

-1/4k-9/4=-4-1/2k

We move all terms to the left:

-1/4k-9/4-(-4-1/2k)=0


Domain of the equation: 4k!=0

k!=0/4

k!=0

k∈R



Domain of the equation: 2k)!=0

k!=0/1

k!=0

k∈R


We add all the numbers together, and all the variables

-1/4k-(-1/2k-4)-9/4=0

We get rid of parentheses

-1/4k+1/2k+4-9/4=0

We calculate fractions


(-2k)/128k^2+64k/128k^2+(-18k)/128k^2+4=0

We multiply all the terms by the denominator


(-2k)+64k+(-18k)+4*128k^2=0

We add all the numbers together, and all the variables

64k+(-2k)+(-18k)+4*128k^2=0

Wy multiply elements

512k^2+64k+(-2k)+(-18k)=0

We get rid of parentheses

512k^2+64k-2k-18k=0

We add all the numbers together, and all the variables

512k^2+44k=0

a = 512; b = 44; c = 0;
Δ = b2-4ac
Δ = 442-4·512·0
Δ = 1936
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1936}=44$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(44)-44}{2*512}=\frac{-88}{1024}
=-11/128
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(44)+44}{2*512}=\frac{0}{1024}
=0
$