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x(120-4x)=600
We move all terms to the left:
x(120-4x)-(600)=0
We add all the numbers together, and all the variables
x(-4x+120)-600=0
We multiply parentheses
-4x^2+120x-600=0
a = -4; b = 120; c = -600;
Δ = b2-4ac
Δ = 1202-4·(-4)·(-600)
Δ = 4800
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{4800}=\sqrt{1600*3}=\sqrt{1600}*\sqrt{3}=40\sqrt{3}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(120)-40\sqrt{3}}{2*-4}=\frac{-120-40\sqrt{3}}{-8} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(120)+40\sqrt{3}}{2*-4}=\frac{-120+40\sqrt{3}}{-8} $
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