3x(x+6)-2x=x-18

Solution for 3x(x+6)-2x=x-18 equation:

3x(x+6)-2x=x-18

We move all terms to the left:

3x(x+6)-2x-(x-18)=0

We add all the numbers together, and all the variables

-2x+3x(x+6)-(x-18)=0

We multiply parentheses

3x^2-2x+18x-(x-18)=0

We get rid of parentheses

3x^2-2x+18x-x+18=0

We add all the numbers together, and all the variables

3x^2+15x+18=0

a = 3; b = 15; c = +18;
Δ = b2-4ac
Δ = 152-4·3·18
Δ = 9
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{9}=3$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(15)-3}{2*3}=\frac{-18}{6}
=-3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(15)+3}{2*3}=\frac{-12}{6}
=-2
$