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6x(x-9)=180
We move all terms to the left:
6x(x-9)-(180)=0
We multiply parentheses
6x^2-54x-180=0
a = 6; b = -54; c = -180;
Δ = b2-4ac
Δ = -542-4·6·(-180)
Δ = 7236
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{7236}=\sqrt{36*201}=\sqrt{36}*\sqrt{201}=6\sqrt{201}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-54)-6\sqrt{201}}{2*6}=\frac{54-6\sqrt{201}}{12} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-54)+6\sqrt{201}}{2*6}=\frac{54+6\sqrt{201}}{12} $
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