0=4x^2-320x+3000

Solution for 0=4x^2-320x+3000 equation:

0=4x^2-320x+3000

We move all terms to the left:

0-(4x^2-320x+3000)=0

We add all the numbers together, and all the variables

-(4x^2-320x+3000)=0

We get rid of parentheses

-4x^2+320x-3000=0

a = -4; b = 320; c = -3000;
Δ = b2-4ac
Δ = 3202-4·(-4)·(-3000)
Δ = 54400
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:

$\sqrt{\Delta}=\sqrt{54400}=\sqrt{1600*34}=\sqrt{1600}*\sqrt{34}=40\sqrt{34}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(320)-40\sqrt{34}}{2*-4}=\frac{-320-40\sqrt{34}}{-8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(320)+40\sqrt{34}}{2*-4}=\frac{-320+40\sqrt{34}}{-8}
$