(X)(x+8)=(x+5)(2x-8)

Solution for (X)(x+8)=(x+5)(2x-8) equation:

(X)(X+8)=(X+5)(2X-8)

We move all terms to the left:

(X)(X+8)-((X+5)(2X-8))=0

We multiply parentheses

X^2+8X-((X+5)(2X-8))=0

We multiply parentheses ..

X^2-((+2X^2-8X+10X-40))+8X=0


We calculate terms in parentheses: -((+2X^2-8X+10X-40)), so:

(+2X^2-8X+10X-40)

We get rid of parentheses

2X^2-8X+10X-40

We add all the numbers together, and all the variables

2X^2+2X-40

Back to the equation:

-(2X^2+2X-40)


We add all the numbers together, and all the variables

X^2+8X-(2X^2+2X-40)=0

We get rid of parentheses

X^2-2X^2+8X-2X+40=0

We add all the numbers together, and all the variables

-1X^2+6X+40=0

a = -1; b = 6; c = +40;
Δ = b2-4ac
Δ = 62-4·(-1)·40
Δ = 196
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{196}=14$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-14}{2*-1}=\frac{-20}{-2}
=+10
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+14}{2*-1}=\frac{8}{-2}
=-4
$