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36000-300x=6x^2
We move all terms to the left:
36000-300x-(6x^2)=0
determiningTheFunctionDomain -6x^2-300x+36000=0
a = -6; b = -300; c = +36000;
Δ = b2-4ac
Δ = -3002-4·(-6)·36000
Δ = 954000
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{954000}=\sqrt{3600*265}=\sqrt{3600}*\sqrt{265}=60\sqrt{265}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-300)-60\sqrt{265}}{2*-6}=\frac{300-60\sqrt{265}}{-12} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-300)+60\sqrt{265}}{2*-6}=\frac{300+60\sqrt{265}}{-12} $
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