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

Solution for 9=x(2x+3)-2x equation:

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

We move all terms to the left:

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


We calculate terms in parentheses: -(x(2x+3)-2x), so:

x(2x+3)-2x

We add all the numbers together, and all the variables

-2x+x(2x+3)

We multiply parentheses

2x^2-2x+3x

We add all the numbers together, and all the variables

2x^2+x

Back to the equation:

-(2x^2+x)


We get rid of parentheses

-2x^2-x+9=0

We add all the numbers together, and all the variables

-2x^2-1x+9=0

a = -2; b = -1; c = +9;
Δ = b2-4ac
Δ = -12-4·(-2)·9
Δ = 73
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{-(-1)-\sqrt{73}}{2*-2}=\frac{1-\sqrt{73}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+\sqrt{73}}{2*-2}=\frac{1+\sqrt{73}}{-4}
$