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6x(3x-2)=8
We move all terms to the left:
6x(3x-2)-(8)=0
We multiply parentheses
18x^2-12x-8=0
a = 18; b = -12; c = -8;
Δ = b2-4ac
Δ = -122-4·18·(-8)
Δ = 720
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{720}=\sqrt{144*5}=\sqrt{144}*\sqrt{5}=12\sqrt{5}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-12\sqrt{5}}{2*18}=\frac{12-12\sqrt{5}}{36} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+12\sqrt{5}}{2*18}=\frac{12+12\sqrt{5}}{36} $
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