X(40-2X)+X(40-2X)+53.3(40-2X)+53.3(40-2X)+53.3(20)=s

Solution for X(40-2X)+X(40-2X)+53.3(40-2X)+53.3(40-2X)+53.3(20)=s equation:

X(40-2X)+X(40-2X)+53.3(40-2X)+53.3(40-2X)+53.3(20)=X

We move all terms to the left:

X(40-2X)+X(40-2X)+53.3(40-2X)+53.3(40-2X)+53.3(20)-(X)=0

We add all the numbers together, and all the variables

X(-2X+40)+X(-2X+40)+53.3(-2X+40)+53.3(-2X+40)-X+53.320=0

We add all the numbers together, and all the variables

-1X+X(-2X+40)+X(-2X+40)+53.3(-2X+40)+53.3(-2X+40)+53.32=0

We multiply parentheses

-2X^2-2X^2-1X+40X+40X-106.6X-106.6X+2132+2132+53.32=0

We add all the numbers together, and all the variables

-4X^2-134.2X+4317.32=0

a = -4; b = -134.2; c = +4317.32;
Δ = b2-4ac
Δ = -134.22-4·(-4)·4317.32
Δ = 87086.76
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-134.2)-\sqrt{87086.76}}{2*-4}=\frac{134.2-\sqrt{87086.76}}{-8}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-134.2)+\sqrt{87086.76}}{2*-4}=\frac{134.2+\sqrt{87086.76}}{-8}
$