3x^2+2x=1000

Solution for 3x^2+2x=1000 equation:

3x^2+2x=1000

We move all terms to the left:

3x^2+2x-(1000)=0

a = 3; b = 2; c = -1000;
Δ = b2-4ac
Δ = 22-4·3·(-1000)
Δ = 12004
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:

$\sqrt{\Delta}=\sqrt{12004}=\sqrt{4*3001}=\sqrt{4}*\sqrt{3001}=2\sqrt{3001}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-2\sqrt{3001}}{2*3}=\frac{-2-2\sqrt{3001}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2\sqrt{3001}}{2*3}=\frac{-2+2\sqrt{3001}}{6}
$