k+2/5k=12

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

k+2/5k=12

We move all terms to the left:

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


Domain of the equation: 5k!=0

k!=0/5

k!=0

k∈R


We multiply all the terms by the denominator


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

Wy multiply elements

5k^2-60k+2=0

a = 5; b = -60; c = +2;
Δ = b2-4ac
Δ = -602-4·5·2
Δ = 3560
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:

$\sqrt{\Delta}=\sqrt{3560}=\sqrt{4*890}=\sqrt{4}*\sqrt{890}=2\sqrt{890}$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-60)-2\sqrt{890}}{2*5}=\frac{60-2\sqrt{890}}{10}
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-60)+2\sqrt{890}}{2*5}=\frac{60+2\sqrt{890}}{10}
$