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

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

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

We move all terms to the left:

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

We multiply parentheses

-2x^2-4x-(x-18)+3=0

We get rid of parentheses

-2x^2-4x-x+18+3=0

We add all the numbers together, and all the variables

-2x^2-5x+21=0

a = -2; b = -5; c = +21;
Δ = b2-4ac
Δ = -52-4·(-2)·21
Δ = 193
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{-(-5)-\sqrt{193}}{2*-2}=\frac{5-\sqrt{193}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+\sqrt{193}}{2*-2}=\frac{5+\sqrt{193}}{-4}
$