(38*32)-(32-2x)(38-2x)=600

Solution for (38*32)-(32-2x)(38-2x)=600 equation:

(38*32)-(32-2x)(38-2x)=600

We move all terms to the left:

(38*32)-(32-2x)(38-2x)-(600)=0

determiningTheFunctionDomain
-(32-2x)(38-2x)-600+(38*32)=0

We add all the numbers together, and all the variables

-(-2x+32)(-2x+38)-600+1216=0

We add all the numbers together, and all the variables

-(-2x+32)(-2x+38)+616=0

We multiply parentheses ..

-(+4x^2-76x-64x+1216)+616=0

We get rid of parentheses

-4x^2+76x+64x-1216+616=0

We add all the numbers together, and all the variables

-4x^2+140x-600=0

a = -4; b = 140; c = -600;
Δ = b2-4ac
Δ = 1402-4·(-4)·(-600)
Δ = 10000
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{10000}=100$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(140)-100}{2*-4}=\frac{-240}{-8}
=+30
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(140)+100}{2*-4}=\frac{-40}{-8}
=+5
$