6x^2=4500

Solution for 6x^2=4500 equation:

6x^2=4500

We move all terms to the left:

6x^2-(4500)=0

a = 6; b = 0; c = -4500;
Δ = b2-4ac
Δ = 02-4·6·(-4500)
Δ = 108000
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{108000}=\sqrt{3600*30}=\sqrt{3600}*\sqrt{30}=60\sqrt{30}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-60\sqrt{30}}{2*6}=\frac{0-60\sqrt{30}}{12}
=-\frac{60\sqrt{30}}{12}
=-5\sqrt{30}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+60\sqrt{30}}{2*6}=\frac{0+60\sqrt{30}}{12}
=\frac{60\sqrt{30}}{12}
=5\sqrt{30}
$