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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} $
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