-4x(9+x)=-16

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



-4x(9+x)=-16
We move all terms to the left:
-4x(9+x)-(-16)=0
We add all the numbers together, and all the variables
-4x(x+9)-(-16)=0
We add all the numbers together, and all the variables
-4x(x+9)+16=0
We multiply parentheses
-4x^2-36x+16=0
a = -4; b = -36; c = +16;
Δ = b2-4ac
Δ = -362-4·(-4)·16
Δ = 1552
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:
$\sqrt{\Delta}=\sqrt{1552}=\sqrt{16*97}=\sqrt{16}*\sqrt{97}=4\sqrt{97}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-36)-4\sqrt{97}}{2*-4}=\frac{36-4\sqrt{97}}{-8} $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-36)+4\sqrt{97}}{2*-4}=\frac{36+4\sqrt{97}}{-8} $

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