18+6x-12=-4x(2-x)+9x

Solution for 18+6x-12=-4x(2-x)+9x equation:

18+6x-12=-4x(2-x)+9x

We move all terms to the left:

18+6x-12-(-4x(2-x)+9x)=0

We add all the numbers together, and all the variables

6x-(-4x(-1x+2)+9x)+18-12=0

We add all the numbers together, and all the variables

6x-(-4x(-1x+2)+9x)+6=0


We calculate terms in parentheses: -(-4x(-1x+2)+9x), so:

-4x(-1x+2)+9x

We add all the numbers together, and all the variables

9x-4x(-1x+2)

We multiply parentheses

4x^2+9x-8x

We add all the numbers together, and all the variables

4x^2+x

Back to the equation:

-(4x^2+x)


We get rid of parentheses

-4x^2+6x-x+6=0

We add all the numbers together, and all the variables

-4x^2+5x+6=0

a = -4; b = 5; c = +6;
Δ = b2-4ac
Δ = 52-4·(-4)·6
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*-4}=\frac{-16}{-8}
=+2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+11}{2*-4}=\frac{6}{-8}
=-3/4
$