3x(x+7)=-x-3

Solution for 3x(x+7)=-x-3 equation:

3x(x+7)=-x-3

We move all terms to the left:

3x(x+7)-(-x-3)=0

We add all the numbers together, and all the variables

3x(x+7)-(-1x-3)=0

We multiply parentheses

3x^2+21x-(-1x-3)=0

We get rid of parentheses

3x^2+21x+1x+3=0

We add all the numbers together, and all the variables

3x^2+22x+3=0

a = 3; b = 22; c = +3;
Δ = b2-4ac
Δ = 222-4·3·3
Δ = 448
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{448}=\sqrt{64*7}=\sqrt{64}*\sqrt{7}=8\sqrt{7}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(22)-8\sqrt{7}}{2*3}=\frac{-22-8\sqrt{7}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(22)+8\sqrt{7}}{2*3}=\frac{-22+8\sqrt{7}}{6}
$