6x^2=1600

Solution for 6x^2=1600 equation:

6x^2=1600

We move all terms to the left:

6x^2-(1600)=0

a = 6; b = 0; c = -1600;
Δ = b2-4ac
Δ = 02-4·6·(-1600)
Δ = 38400
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:

$\sqrt{\Delta}=\sqrt{38400}=\sqrt{6400*6}=\sqrt{6400}*\sqrt{6}=80\sqrt{6}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-80\sqrt{6}}{2*6}=\frac{0-80\sqrt{6}}{12}
=-\frac{80\sqrt{6}}{12}
=-\frac{20\sqrt{6}}{3}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+80\sqrt{6}}{2*6}=\frac{0+80\sqrt{6}}{12}
=\frac{80\sqrt{6}}{12}
=\frac{20\sqrt{6}}{3}
$