-1(2/3)=5k

Solution for -1(2/3)=5k equation:

-1(2/3)=5k

We move all terms to the left:

-1(2/3)-(5k)=0

We add all the numbers together, and all the variables

-5k-1(+2/3)=0

We multiply all the terms by the denominator


-5k*3)-1(+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}
$