10+k-1/3k=0

Solution for 10+k-1/3k=0 equation:

10+k-1/3k=0


Domain of the equation: 3k!=0

k!=0/3

k!=0

k∈R


We multiply all the terms by the denominator


k*3k+10*3k-1=0

Wy multiply elements

3k^2+30k-1=0

a = 3; b = 30; c = -1;
Δ = b2-4ac
Δ = 302-4·3·(-1)
Δ = 912
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:

$\sqrt{\Delta}=\sqrt{912}=\sqrt{16*57}=\sqrt{16}*\sqrt{57}=4\sqrt{57}$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(30)-4\sqrt{57}}{2*3}=\frac{-30-4\sqrt{57}}{6}
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(30)+4\sqrt{57}}{2*3}=\frac{-30+4\sqrt{57}}{6}
$