3x(x+2)+x=30-2x

Solution for 3x(x+2)+x=30-2x equation:

3x(x+2)+x=30-2x

We move all terms to the left:

3x(x+2)+x-(30-2x)=0

We add all the numbers together, and all the variables

3x(x+2)+x-(-2x+30)=0

We add all the numbers together, and all the variables

x+3x(x+2)-(-2x+30)=0

We multiply parentheses

3x^2+x+6x-(-2x+30)=0

We get rid of parentheses

3x^2+x+6x+2x-30=0

We add all the numbers together, and all the variables

3x^2+9x-30=0

a = 3; b = 9; c = -30;
Δ = b2-4ac
Δ = 92-4·3·(-30)
Δ = 441
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{441}=21$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(9)-21}{2*3}=\frac{-30}{6}
=-5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+21}{2*3}=\frac{12}{6}
=2
$