(X^2-3x=5x-15)(x+1)

Solution for (X^2-3x=5x-15)(x+1) equation:

(X^2-3X=5X-15)(X+1)

We move all terms to the left:

(X^2-3X-(5X-15)(X+1))=0

We multiply parentheses ..

(X^2-3X-(+5X^2+5X-15X-15))=0


We calculate terms in parentheses: +(X^2-3X-(+5X^2+5X-15X-15)), so:

X^2-3X-(+5X^2+5X-15X-15)

determiningTheFunctionDomain
X^2-(+5X^2+5X-15X-15)-3X

We get rid of parentheses

X^2-5X^2-5X+15X-3X+15

We add all the numbers together, and all the variables

-4X^2+7X+15

Back to the equation:

+(-4X^2+7X+15)


We get rid of parentheses

-4X^2+7X+15=0

a = -4; b = 7; c = +15;
Δ = b2-4ac
Δ = 72-4·(-4)·15
Δ = 289
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{289}=17$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(7)-17}{2*-4}=\frac{-24}{-8}
=+3
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+17}{2*-4}=\frac{10}{-8}
=-1+1/4
$