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

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

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

We move all terms to the left:

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

We multiply parentheses

-4x^2+9x-36x-36-4=0

We add all the numbers together, and all the variables

-4x^2-27x-40=0

a = -4; b = -27; c = -40;
Δ = b2-4ac
Δ = -272-4·(-4)·(-40)
Δ = 89
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{-(-27)-\sqrt{89}}{2*-4}=\frac{27-\sqrt{89}}{-8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-27)+\sqrt{89}}{2*-4}=\frac{27+\sqrt{89}}{-8}
$