066x*x=1000

Solution for 066x*x=1000 equation:

066x*x=1000

We move all terms to the left:

066x*x-(1000)=0

Wy multiply elements

66x^2-1000=0

a = 66; b = 0; c = -1000;
Δ = b2-4ac
Δ = 02-4·66·(-1000)
Δ = 264000
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:

$\sqrt{\Delta}=\sqrt{264000}=\sqrt{1600*165}=\sqrt{1600}*\sqrt{165}=40\sqrt{165}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-40\sqrt{165}}{2*66}=\frac{0-40\sqrt{165}}{132}
=-\frac{40\sqrt{165}}{132}
=-\frac{10\sqrt{165}}{33}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+40\sqrt{165}}{2*66}=\frac{0+40\sqrt{165}}{132}
=\frac{40\sqrt{165}}{132}
=\frac{10\sqrt{165}}{33}
$