x(x+2)=-8(x+3)

Solution for x(x+2)=-8(x+3) equation:

x(x+2)=-8(x+3)

We move all terms to the left:

x(x+2)-(-8(x+3))=0

We multiply parentheses

x^2+2x-(-8(x+3))=0


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

-8(x+3)

We multiply parentheses

-8x-24

Back to the equation:

-(-8x-24)


We get rid of parentheses

x^2+2x+8x+24=0

We add all the numbers together, and all the variables

x^2+10x+24=0

a = 1; b = 10; c = +24;
Δ = b2-4ac
Δ = 102-4·1·24
Δ = 4
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4}=2$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-2}{2*1}=\frac{-12}{2}
=-6
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+2}{2*1}=\frac{-8}{2}
=-4
$