54k^2+69=75

Solution for 54k^2+69=75 equation:

54k^2+69=75

We move all terms to the left:

54k^2+69-(75)=0

We add all the numbers together, and all the variables

54k^2-6=0

a = 54; b = 0; c = -6;
Δ = b2-4ac
Δ = 02-4·54·(-6)
Δ = 1296
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1296}=36$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-36}{2*54}=\frac{-36}{108}
=-1/3
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+36}{2*54}=\frac{36}{108}
=1/3
$