4x+3x(36-x)=124

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Solution for 4x+3x(36-x)=124 equation:



4x+3x(36-x)=124
We move all terms to the left:
4x+3x(36-x)-(124)=0
We add all the numbers together, and all the variables
4x+3x(-1x+36)-124=0
We multiply parentheses
-3x^2+4x+108x-124=0
We add all the numbers together, and all the variables
-3x^2+112x-124=0
a = -3; b = 112; c = -124;
Δ = b2-4ac
Δ = 1122-4·(-3)·(-124)
Δ = 11056
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:
$\sqrt{\Delta}=\sqrt{11056}=\sqrt{16*691}=\sqrt{16}*\sqrt{691}=4\sqrt{691}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(112)-4\sqrt{691}}{2*-3}=\frac{-112-4\sqrt{691}}{-6} $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(112)+4\sqrt{691}}{2*-3}=\frac{-112+4\sqrt{691}}{-6} $

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