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

Solution for 1/2*k-3=2-3/4*k 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: 2k!=0

k!=0/2

k!=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

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

We get rid of parentheses

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

We calculate fractions


4k/8k^2+6k/8k^2-2-3=0

We add all the numbers together, and all the variables

4k/8k^2+6k/8k^2-5=0

We multiply all the terms by the denominator


4k+6k-5*8k^2=0

We add all the numbers together, and all the variables

10k-5*8k^2=0

Wy multiply elements

-40k^2+10k=0

a = -40; b = 10; c = 0;
Δ = b2-4ac
Δ = 102-4·(-40)·0
Δ = 100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{100}=10$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-10}{2*-40}=\frac{-20}{-80}
=1/4
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+10}{2*-40}=\frac{0}{-80}
=0
$