1000x^2-100x=3000

Solution for 1000x^2-100x=3000 equation:

1000x^2-100x=3000

We move all terms to the left:

1000x^2-100x-(3000)=0

a = 1000; b = -100; c = -3000;
Δ = b2-4ac
Δ = -1002-4·1000·(-3000)
Δ = 12010000
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:

$\sqrt{\Delta}=\sqrt{12010000}=\sqrt{10000*1201}=\sqrt{10000}*\sqrt{1201}=100\sqrt{1201}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-100)-100\sqrt{1201}}{2*1000}=\frac{100-100\sqrt{1201}}{2000}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-100)+100\sqrt{1201}}{2*1000}=\frac{100+100\sqrt{1201}}{2000}
$