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

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

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

We move all terms to the left:

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

We multiply parentheses

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

We get rid of parentheses

-2x^2-6x-x+18+3=0

We add all the numbers together, and all the variables

-2x^2-7x+21=0

a = -2; b = -7; c = +21;
Δ = b2-4ac
Δ = -72-4·(-2)·21
Δ = 217
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-7)-\sqrt{217}}{2*-2}=\frac{7-\sqrt{217}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+\sqrt{217}}{2*-2}=\frac{7+\sqrt{217}}{-4}
$