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

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

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

We move all terms to the left:

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

We add all the numbers together, and all the variables

(X+2)(3X+10)-(-1X)=0

We get rid of parentheses

(X+2)(3X+10)+1X=0

We multiply parentheses ..

(+3X^2+10X+6X+20)+1X=0

We add all the numbers together, and all the variables

(+3X^2+10X+6X+20)+X=0

We get rid of parentheses

3X^2+10X+6X+X+20=0

We add all the numbers together, and all the variables

3X^2+17X+20=0

a = 3; b = 17; c = +20;
Δ = b2-4ac
Δ = 172-4·3·20
Δ = 49
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{49}=7$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(17)-7}{2*3}=\frac{-24}{6}
=-4
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(17)+7}{2*3}=\frac{-10}{6}
=-1+2/3
$