4k-10/k=10

Solution for 4k-10/k=10 equation:

4k-10/k=10

We move all terms to the left:

4k-10/k-(10)=0


Domain of the equation: k!=0

k∈R


We multiply all the terms by the denominator


4k*k-10*k-10=0

We add all the numbers together, and all the variables

-10k+4k*k-10=0

Wy multiply elements

4k^2-10k-10=0

a = 4; b = -10; c = -10;
Δ = b2-4ac
Δ = -102-4·4·(-10)
Δ = 260
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:

$\sqrt{\Delta}=\sqrt{260}=\sqrt{4*65}=\sqrt{4}*\sqrt{65}=2\sqrt{65}$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-2\sqrt{65}}{2*4}=\frac{10-2\sqrt{65}}{8}
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+2\sqrt{65}}{2*4}=\frac{10+2\sqrt{65}}{8}
$