k-5/2k=12

Solution for k-5/2k=12 equation:

k-5/2k=12

We move all terms to the left:

k-5/2k-(12)=0


Domain of the equation: 2k!=0

k!=0/2

k!=0

k∈R


We multiply all the terms by the denominator


k*2k-12*2k-5=0

Wy multiply elements

2k^2-24k-5=0

a = 2; b = -24; c = -5;
Δ = b2-4ac
Δ = -242-4·2·(-5)
Δ = 616
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:

$\sqrt{\Delta}=\sqrt{616}=\sqrt{4*154}=\sqrt{4}*\sqrt{154}=2\sqrt{154}$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-24)-2\sqrt{154}}{2*2}=\frac{24-2\sqrt{154}}{4}
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-24)+2\sqrt{154}}{2*2}=\frac{24+2\sqrt{154}}{4}
$