x*65x=2000

Solution for x*65x=2000 equation:

x*65x=2000

We move all terms to the left:

x*65x-(2000)=0

Wy multiply elements

65x^2-2000=0

a = 65; b = 0; c = -2000;
Δ = b2-4ac
Δ = 02-4·65·(-2000)
Δ = 520000
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:

$\sqrt{\Delta}=\sqrt{520000}=\sqrt{40000*13}=\sqrt{40000}*\sqrt{13}=200\sqrt{13}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-200\sqrt{13}}{2*65}=\frac{0-200\sqrt{13}}{130}
=-\frac{200\sqrt{13}}{130}
=-\frac{20\sqrt{13}}{13}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+200\sqrt{13}}{2*65}=\frac{0+200\sqrt{13}}{130}
=\frac{200\sqrt{13}}{130}
=\frac{20\sqrt{13}}{13}
$