3946.41=2392.00679512+11.81424805*x+-0.01527339*x^2

Solution for 3946.41=2392.00679512+11.81424805*x+-0.01527339*x^2 equation:

3946.41=2392.00679512+11.81424805x+-0.01527339x^2

We move all terms to the left:

3946.41-(2392.00679512+11.81424805x+-0.01527339x^2)=0

We use the square of the difference formula

-(2392.00679512+11.81424805x-0.01527339x^2)+3946.41=0

We get rid of parentheses

0.01527339x^2-11.81424805x-2392.00679512+3946.41=0

We add all the numbers together, and all the variables

0.01527339x^2-11.81424805x+1554.40320488=0

a = 0.01527339; b = -11.81424805; c = +1554.40320488;
Δ = b2-4ac
Δ = -11.814248052-4·0.01527339·1554.40320488
Δ = 44.6124315254
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-11.81424805)-\sqrt{44.6124315254}}{2*0.01527339}=\frac{11.81424805-\sqrt{44.6124315254}}{0.03054678}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-11.81424805)+\sqrt{44.6124315254}}{2*0.01527339}=\frac{11.81424805+\sqrt{44.6124315254}}{0.03054678}
$