6x^2=75

Solution for 6x^2=75 equation:

6x^2=75

We move all terms to the left:

6x^2-(75)=0

a = 6; b = 0; c = -75;
Δ = b2-4ac
Δ = 02-4·6·(-75)
Δ = 1800
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:

$\sqrt{\Delta}=\sqrt{1800}=\sqrt{900*2}=\sqrt{900}*\sqrt{2}=30\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-30\sqrt{2}}{2*6}=\frac{0-30\sqrt{2}}{12}
=-\frac{30\sqrt{2}}{12}
=-\frac{5\sqrt{2}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+30\sqrt{2}}{2*6}=\frac{0+30\sqrt{2}}{12}
=\frac{30\sqrt{2}}{12}
=\frac{5\sqrt{2}}{2}
$