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6x(9-x)=30
We move all terms to the left:
6x(9-x)-(30)=0
We add all the numbers together, and all the variables
6x(-1x+9)-30=0
We multiply parentheses
-6x^2+54x-30=0
a = -6; b = 54; c = -30;
Δ = b2-4ac
Δ = 542-4·(-6)·(-30)
Δ = 2196
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{2196}=\sqrt{36*61}=\sqrt{36}*\sqrt{61}=6\sqrt{61}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(54)-6\sqrt{61}}{2*-6}=\frac{-54-6\sqrt{61}}{-12} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(54)+6\sqrt{61}}{2*-6}=\frac{-54+6\sqrt{61}}{-12} $
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