1/2*k=5

Solution for 1/2*k=5 equation:

1/2*k=5

We move all terms to the left:

1/2*k-(5)=0


Domain of the equation: 2*k!=0

k!=0/1

k!=0

k∈R


We multiply all the terms by the denominator


-5*2*k+1=0

Wy multiply elements

-10k*k+1=0

Wy multiply elements

-10k^2+1=0

a = -10; b = 0; c = +1;
Δ = b2-4ac
Δ = 02-4·(-10)·1
Δ = 40
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:

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