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12x(3x-7)=6
We move all terms to the left:
12x(3x-7)-(6)=0
We multiply parentheses
36x^2-84x-6=0
a = 36; b = -84; c = -6;
Δ = b2-4ac
Δ = -842-4·36·(-6)
Δ = 7920
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{7920}=\sqrt{144*55}=\sqrt{144}*\sqrt{55}=12\sqrt{55}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-84)-12\sqrt{55}}{2*36}=\frac{84-12\sqrt{55}}{72} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-84)+12\sqrt{55}}{2*36}=\frac{84+12\sqrt{55}}{72} $
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