3/5*k=225

Solution for 3/5*k=225 equation:

3/5*k=225

We move all terms to the left:

3/5*k-(225)=0


Domain of the equation: 5*k!=0

k!=0/1

k!=0

k∈R


We multiply all the terms by the denominator


-225*5*k+3=0

Wy multiply elements

-1125k*k+3=0

Wy multiply elements

-1125k^2+3=0

a = -1125; b = 0; c = +3;
Δ = b2-4ac
Δ = 02-4·(-1125)·3
Δ = 13500
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:

$\sqrt{\Delta}=\sqrt{13500}=\sqrt{900*15}=\sqrt{900}*\sqrt{15}=30\sqrt{15}$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-30\sqrt{15}}{2*-1125}=\frac{0-30\sqrt{15}}{-2250}
=-\frac{30\sqrt{15}}{-2250}
=-\frac{\sqrt{15}}{-75}
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+30\sqrt{15}}{2*-1125}=\frac{0+30\sqrt{15}}{-2250}
=\frac{30\sqrt{15}}{-2250}
=\frac{\sqrt{15}}{-75}
$