0.5k-3=2-3/4k

Solution for 0.5k-3=2-3/4k equation:

0.5k-3=2-3/4k

We move all terms to the left:

0.5k-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

0.5k-(-3/4k+2)-3=0

We get rid of parentheses

0.5k+3/4k-2-3=0

We multiply all the terms by the denominator


(0.5k)*4k-2*4k-3*4k+3=0

We add all the numbers together, and all the variables

(+0.5k)*4k-2*4k-3*4k+3=0

We multiply parentheses

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

Wy multiply elements

0k^2-8k-12k+3=0

We add all the numbers together, and all the variables

k^2-20k+3=0

a = 1; b = -20; c = +3;
Δ = b2-4ac
Δ = -202-4·1·3
Δ = 388
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:

$\sqrt{\Delta}=\sqrt{388}=\sqrt{4*97}=\sqrt{4}*\sqrt{97}=2\sqrt{97}$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-20)-2\sqrt{97}}{2*1}=\frac{20-2\sqrt{97}}{2}
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-20)+2\sqrt{97}}{2*1}=\frac{20+2\sqrt{97}}{2}
$