x(x+3)=-2(3x+10)

Solution for x(x+3)=-2(3x+10) equation:

x(x+3)=-2(3x+10)

We move all terms to the left:

x(x+3)-(-2(3x+10))=0

We multiply parentheses

x^2+3x-(-2(3x+10))=0


We calculate terms in parentheses: -(-2(3x+10)), so:

-2(3x+10)

We multiply parentheses

-6x-20

Back to the equation:

-(-6x-20)


We get rid of parentheses

x^2+3x+6x+20=0

We add all the numbers together, and all the variables

x^2+9x+20=0

a = 1; b = 9; c = +20;
Δ = b2-4ac
Δ = 92-4·1·20
Δ = 1
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1}=1$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(9)-1}{2*1}=\frac{-10}{2}
=-5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+1}{2*1}=\frac{-8}{2}
=-4
$