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6x(9x-3)=147
We move all terms to the left:
6x(9x-3)-(147)=0
We multiply parentheses
54x^2-18x-147=0
a = 54; b = -18; c = -147;
Δ = b2-4ac
Δ = -182-4·54·(-147)
Δ = 32076
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{32076}=\sqrt{2916*11}=\sqrt{2916}*\sqrt{11}=54\sqrt{11}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-18)-54\sqrt{11}}{2*54}=\frac{18-54\sqrt{11}}{108} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-18)+54\sqrt{11}}{2*54}=\frac{18+54\sqrt{11}}{108} $
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