(5/6)k+(2/3)=4/3

Solution for (5/6)k+(2/3)=4/3 equation:

(5/6)k+(2/3)=4/3

We move all terms to the left:

(5/6)k+(2/3)-(4/3)=0


Domain of the equation: 6)k!=0

k!=0/1

k!=0

k∈R


We add all the numbers together, and all the variables

(+5/6)k+(+2/3)-(+4/3)=0

We multiply parentheses

5k^2+(+2/3)-(+4/3)=0

We get rid of parentheses

5k^2+2/3-4/3=0

We multiply all the terms by the denominator


5k^2*3+2-4=0

We add all the numbers together, and all the variables

5k^2*3-2=0

Wy multiply elements

15k^2-2=0

a = 15; b = 0; c = -2;
Δ = b2-4ac
Δ = 02-4·15·(-2)
Δ = 120
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:

$\sqrt{\Delta}=\sqrt{120}=\sqrt{4*30}=\sqrt{4}*\sqrt{30}=2\sqrt{30}$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{30}}{2*15}=\frac{0-2\sqrt{30}}{30}
=-\frac{2\sqrt{30}}{30}
=-\frac{\sqrt{30}}{15}
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{30}}{2*15}=\frac{0+2\sqrt{30}}{30}
=\frac{2\sqrt{30}}{30}
=\frac{\sqrt{30}}{15}
$