5k-2/3k=7

Solution for 5k-2/3k=7 equation:

5k-2/3k=7

We move all terms to the left:

5k-2/3k-(7)=0


Domain of the equation: 3k!=0

k!=0/3

k!=0

k∈R


We multiply all the terms by the denominator


5k*3k-7*3k-2=0

Wy multiply elements

15k^2-21k-2=0

a = 15; b = -21; c = -2;
Δ = b2-4ac
Δ = -212-4·15·(-2)
Δ = 561
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-21)-\sqrt{561}}{2*15}=\frac{21-\sqrt{561}}{30}
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-21)+\sqrt{561}}{2*15}=\frac{21+\sqrt{561}}{30}
$