(2/3)k-8=52

Solution for (2/3)k-8=52 equation:

(2/3)k-8=52

We move all terms to the left:

(2/3)k-8-(52)=0


Domain of the equation: 3)k!=0

k!=0/1

k!=0

k∈R


We add all the numbers together, and all the variables

(+2/3)k-8-52=0

We add all the numbers together, and all the variables

(+2/3)k-60=0

We multiply parentheses

2k^2-60=0

a = 2; b = 0; c = -60;
Δ = b2-4ac
Δ = 02-4·2·(-60)
Δ = 480
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:

$\sqrt{\Delta}=\sqrt{480}=\sqrt{16*30}=\sqrt{16}*\sqrt{30}=4\sqrt{30}$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{30}}{2*2}=\frac{0-4\sqrt{30}}{4}
=-\frac{4\sqrt{30}}{4}
=-\sqrt{30}
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{30}}{2*2}=\frac{0+4\sqrt{30}}{4}
=\frac{4\sqrt{30}}{4}
=\sqrt{30}
$