368=8X(40+y)

Solution for 368=8X(40+y) equation:

368=8X(40+X)

We move all terms to the left:

368-(8X(40+X))=0

We add all the numbers together, and all the variables

-(8X(X+40))+368=0


We calculate terms in parentheses: -(8X(X+40)), so:

8X(X+40)

We multiply parentheses

8X^2+320X

Back to the equation:

-(8X^2+320X)


We get rid of parentheses

-8X^2-320X+368=0

a = -8; b = -320; c = +368;
Δ = b2-4ac
Δ = -3202-4·(-8)·368
Δ = 114176
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:

$\sqrt{\Delta}=\sqrt{114176}=\sqrt{256*446}=\sqrt{256}*\sqrt{446}=16\sqrt{446}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-320)-16\sqrt{446}}{2*-8}=\frac{320-16\sqrt{446}}{-16}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-320)+16\sqrt{446}}{2*-8}=\frac{320+16\sqrt{446}}{-16}
$