18+16x-12=-4x(2-x)+9x

Solution for 18+16x-12=-4x(2-x)+9x equation:

18+16x-12=-4x(2-x)+9x

We move all terms to the left:

18+16x-12-(-4x(2-x)+9x)=0

We add all the numbers together, and all the variables

16x-(-4x(-1x+2)+9x)+18-12=0

We add all the numbers together, and all the variables

16x-(-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+16x-x+6=0

We add all the numbers together, and all the variables

-4x^2+15x+6=0

a = -4; b = 15; c = +6;
Δ = b2-4ac
Δ = 152-4·(-4)·6
Δ = 321
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{-(15)-\sqrt{321}}{2*-4}=\frac{-15-\sqrt{321}}{-8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(15)+\sqrt{321}}{2*-4}=\frac{-15+\sqrt{321}}{-8}
$