45k^2-125=0

Solution for 45k^2-125=0 equation:

45k^2-125=0

a = 45; b = 0; c = -125;
Δ = b2-4ac
Δ = 02-4·45·(-125)
Δ = 22500
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{22500}=150$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-150}{2*45}=\frac{-150}{90}
=-1+2/3
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+150}{2*45}=\frac{150}{90}
=1+2/3
$