9(x-9)-3=-4x(2x+4)

Solution for 9(x-9)-3=-4x(2x+4) equation:

9(x-9)-3=-4x(2x+4)

We move all terms to the left:

9(x-9)-3-(-4x(2x+4))=0

We multiply parentheses

9x-(-4x(2x+4))-81-3=0


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

-4x(2x+4)

We multiply parentheses

-8x^2-16x

Back to the equation:

-(-8x^2-16x)


We add all the numbers together, and all the variables

-(-8x^2-16x)+9x-84=0

We get rid of parentheses

8x^2+16x+9x-84=0

We add all the numbers together, and all the variables

8x^2+25x-84=0

a = 8; b = 25; c = -84;
Δ = b2-4ac
Δ = 252-4·8·(-84)
Δ = 3313
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{-(25)-\sqrt{3313}}{2*8}=\frac{-25-\sqrt{3313}}{16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(25)+\sqrt{3313}}{2*8}=\frac{-25+\sqrt{3313}}{16}
$