10830-3x^2=2x

Solution for 10830-3x^2=2x equation:

10830-3x^2=2x

We move all terms to the left:

10830-3x^2-(2x)=0

a = -3; b = -2; c = +10830;
Δ = b2-4ac
Δ = -22-4·(-3)·10830
Δ = 129964
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:

$\sqrt{\Delta}=\sqrt{129964}=\sqrt{4*32491}=\sqrt{4}*\sqrt{32491}=2\sqrt{32491}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-2\sqrt{32491}}{2*-3}=\frac{2-2\sqrt{32491}}{-6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+2\sqrt{32491}}{2*-3}=\frac{2+2\sqrt{32491}}{-6}
$