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3x(84-x)=180
We move all terms to the left:
3x(84-x)-(180)=0
We add all the numbers together, and all the variables
3x(-1x+84)-180=0
We multiply parentheses
-3x^2+252x-180=0
a = -3; b = 252; c = -180;
Δ = b2-4ac
Δ = 2522-4·(-3)·(-180)
Δ = 61344
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{61344}=\sqrt{144*426}=\sqrt{144}*\sqrt{426}=12\sqrt{426}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(252)-12\sqrt{426}}{2*-3}=\frac{-252-12\sqrt{426}}{-6} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(252)+12\sqrt{426}}{2*-3}=\frac{-252+12\sqrt{426}}{-6} $
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