(X-3)(x=8)(x-5)=360

Solution for (X-3)(x=8)(x-5)=360 equation:

(X-3)(X=8)(X-5)=360

We move all terms to the left:

(X-3)(X-(8)(X-5))=0


We calculate terms in parentheses: +(X-3)(X-8(X-5)), so:

X-3)(X-8(X-5)

We multiply parentheses

X-3)(X-8X+40

We add all the numbers together, and all the variables

-7X-3)(X+40

Back to the equation:

+(-7X-3)(X+40)


We multiply parentheses ..

(-7X^2-280X-3X-120)=0

We get rid of parentheses

-7X^2-280X-3X-120=0

We add all the numbers together, and all the variables

-7X^2-283X-120=0

a = -7; b = -283; c = -120;
Δ = b2-4ac
Δ = -2832-4·(-7)·(-120)
Δ = 76729
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{76729}=277$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-283)-277}{2*-7}=\frac{6}{-14}
=-3/7
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-283)+277}{2*-7}=\frac{560}{-14}
=-40
$