-13x^2+320x=-28377

Solution for -13x^2+320x=-28377 equation:

-13x^2+320x=-28377

We move all terms to the left:

-13x^2+320x-(-28377)=0

We add all the numbers together, and all the variables

-13x^2+320x+28377=0

a = -13; b = 320; c = +28377;
Δ = b2-4ac
Δ = 3202-4·(-13)·28377
Δ = 1578004
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:

$\sqrt{\Delta}=\sqrt{1578004}=\sqrt{4*394501}=\sqrt{4}*\sqrt{394501}=2\sqrt{394501}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(320)-2\sqrt{394501}}{2*-13}=\frac{-320-2\sqrt{394501}}{-26}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(320)+2\sqrt{394501}}{2*-13}=\frac{-320+2\sqrt{394501}}{-26}
$