8x+4x(300-x)-1600=300

Solution for 8x+4x(300-x)-1600=300 equation:

8x+4x(300-x)-1600=300

We move all terms to the left:

8x+4x(300-x)-1600-(300)=0

We add all the numbers together, and all the variables

8x+4x(-1x+300)-1600-300=0

We add all the numbers together, and all the variables

8x+4x(-1x+300)-1900=0

We multiply parentheses

-4x^2+8x+1200x-1900=0

We add all the numbers together, and all the variables

-4x^2+1208x-1900=0

a = -4; b = 1208; c = -1900;
Δ = b2-4ac
Δ = 12082-4·(-4)·(-1900)
Δ = 1428864
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:

$\sqrt{\Delta}=\sqrt{1428864}=\sqrt{238144*6}=\sqrt{238144}*\sqrt{6}=488\sqrt{6}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1208)-488\sqrt{6}}{2*-4}=\frac{-1208-488\sqrt{6}}{-8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1208)+488\sqrt{6}}{2*-4}=\frac{-1208+488\sqrt{6}}{-8}
$