6s^2+18s^2=540

Solution for 6s^2+18s^2=540 equation:

6s^2+18s^2=540

We move all terms to the left:

6s^2+18s^2-(540)=0

We add all the numbers together, and all the variables

24s^2-540=0

a = 24; b = 0; c = -540;
Δ = b2-4ac
Δ = 02-4·24·(-540)
Δ = 51840
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$s_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$s_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{51840}=\sqrt{5184*10}=\sqrt{5184}*\sqrt{10}=72\sqrt{10}$
$s_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-72\sqrt{10}}{2*24}=\frac{0-72\sqrt{10}}{48}
=-\frac{72\sqrt{10}}{48}
=-\frac{3\sqrt{10}}{2}
$
$s_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+72\sqrt{10}}{2*24}=\frac{0+72\sqrt{10}}{48}
=\frac{72\sqrt{10}}{48}
=\frac{3\sqrt{10}}{2}
$