51-3x^2=0

Solution for 51-3x^2=0 equation:

51-3x^2=0

a = -3; b = 0; c = +51;
Δ = b2-4ac
Δ = 02-4·(-3)·51
Δ = 612
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:

$\sqrt{\Delta}=\sqrt{612}=\sqrt{36*17}=\sqrt{36}*\sqrt{17}=6\sqrt{17}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-6\sqrt{17}}{2*-3}=\frac{0-6\sqrt{17}}{-6}
=-\frac{6\sqrt{17}}{-6}
=-\frac{\sqrt{17}}{-1}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+6\sqrt{17}}{2*-3}=\frac{0+6\sqrt{17}}{-6}
=\frac{6\sqrt{17}}{-6}
=\frac{\sqrt{17}}{-1}
$