k+1.5=4+1/2k

Solution for k+1.5=4+1/2k equation:

k+1.5=4+1/2k

We move all terms to the left:

k+1.5-(4+1/2k)=0


Domain of the equation: 2k)!=0

k!=0/1

k!=0

k∈R


We add all the numbers together, and all the variables

k-(1/2k+4)+1.5=0

We get rid of parentheses

k-1/2k-4+1.5=0

We multiply all the terms by the denominator


k*2k-4*2k+(1.5)*2k-1=0

We multiply parentheses

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

Wy multiply elements

2k^2-8k+3k-1=0

We add all the numbers together, and all the variables

2k^2-5k-1=0

a = 2; b = -5; c = -1;
Δ = b2-4ac
Δ = -52-4·2·(-1)
Δ = 33
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-\sqrt{33}}{2*2}=\frac{5-\sqrt{33}}{4}
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+\sqrt{33}}{2*2}=\frac{5+\sqrt{33}}{4}
$