-4x2-83x=-3+396

Solution for -4x2-83x=-3+396 equation:

-4x^2-83x=-3+396

We move all terms to the left:

-4x^2-83x-(-3+396)=0

We add all the numbers together, and all the variables

-4x^2-83x-393=0

a = -4; b = -83; c = -393;
Δ = b2-4ac
Δ = -832-4·(-4)·(-393)
Δ = 601
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{-(-83)-\sqrt{601}}{2*-4}=\frac{83-\sqrt{601}}{-8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-83)+\sqrt{601}}{2*-4}=\frac{83+\sqrt{601}}{-8}
$