3x*x=5000

Solution for 3x*x=5000 equation:

3x*x=5000

We move all terms to the left:

3x*x-(5000)=0

Wy multiply elements

3x^2-5000=0

a = 3; b = 0; c = -5000;
Δ = b2-4ac
Δ = 02-4·3·(-5000)
Δ = 60000
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:

$\sqrt{\Delta}=\sqrt{60000}=\sqrt{10000*6}=\sqrt{10000}*\sqrt{6}=100\sqrt{6}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-100\sqrt{6}}{2*3}=\frac{0-100\sqrt{6}}{6}
=-\frac{100\sqrt{6}}{6}
=-\frac{50\sqrt{6}}{3}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+100\sqrt{6}}{2*3}=\frac{0+100\sqrt{6}}{6}
=\frac{100\sqrt{6}}{6}
=\frac{50\sqrt{6}}{3}
$