(x-8)(450-3x)=0

Solution for (x-8)(450-3x)=0 equation:

(x-8)(450-3x)=0

We add all the numbers together, and all the variables

(x-8)(-3x+450)=0

We multiply parentheses ..

(-3x^2+450x+24x-3600)=0

We get rid of parentheses

-3x^2+450x+24x-3600=0

We add all the numbers together, and all the variables

-3x^2+474x-3600=0

a = -3; b = 474; c = -3600;
Δ = b2-4ac
Δ = 4742-4·(-3)·(-3600)
Δ = 181476
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{181476}=426$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(474)-426}{2*-3}=\frac{-900}{-6}
=+150
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(474)+426}{2*-3}=\frac{-48}{-6}
=+8
$