x(2x+3)=9x+12-x

Solution for x(2x+3)=9x+12-x equation:

x(2x+3)=9x+12-x

We move all terms to the left:

x(2x+3)-(9x+12-x)=0

We add all the numbers together, and all the variables

x(2x+3)-(8x+12)=0

We multiply parentheses

2x^2+3x-(8x+12)=0

We get rid of parentheses

2x^2+3x-8x-12=0

We add all the numbers together, and all the variables

2x^2-5x-12=0

a = 2; b = -5; c = -12;
Δ = b2-4ac
Δ = -52-4·2·(-12)
Δ = 121
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{121}=11$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-11}{2*2}=\frac{-6}{4}
=-1+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+11}{2*2}=\frac{16}{4}
=4
$