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6x(5x-2)=108
We move all terms to the left:
6x(5x-2)-(108)=0
We multiply parentheses
30x^2-12x-108=0
a = 30; b = -12; c = -108;
Δ = b2-4ac
Δ = -122-4·30·(-108)
Δ = 13104
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{13104}=\sqrt{144*91}=\sqrt{144}*\sqrt{91}=12\sqrt{91}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-12\sqrt{91}}{2*30}=\frac{12-12\sqrt{91}}{60} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+12\sqrt{91}}{2*30}=\frac{12+12\sqrt{91}}{60} $
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