1-2k-3=2-3/4k

Solution for 1-2k-3=2-3/4k equation:

1-2k-3=2-3/4k

We move all terms to the left:

1-2k-3-(2-3/4k)=0


Domain of the equation: 4k)!=0

k!=0/1

k!=0

k∈R


We add all the numbers together, and all the variables

-2k-(-3/4k+2)+1-3=0

We add all the numbers together, and all the variables

-2k-(-3/4k+2)-2=0

We get rid of parentheses

-2k+3/4k-2-2=0

We multiply all the terms by the denominator


-2k*4k-2*4k-2*4k+3=0

Wy multiply elements

-8k^2-8k-8k+3=0

We add all the numbers together, and all the variables

-8k^2-16k+3=0

a = -8; b = -16; c = +3;
Δ = b2-4ac
Δ = -162-4·(-8)·3
Δ = 352
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:

$\sqrt{\Delta}=\sqrt{352}=\sqrt{16*22}=\sqrt{16}*\sqrt{22}=4\sqrt{22}$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-16)-4\sqrt{22}}{2*-8}=\frac{16-4\sqrt{22}}{-16}
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-16)+4\sqrt{22}}{2*-8}=\frac{16+4\sqrt{22}}{-16}
$