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6x(7x-4)=186
We move all terms to the left:
6x(7x-4)-(186)=0
We multiply parentheses
42x^2-24x-186=0
a = 42; b = -24; c = -186;
Δ = b2-4ac
Δ = -242-4·42·(-186)
Δ = 31824
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{31824}=\sqrt{144*221}=\sqrt{144}*\sqrt{221}=12\sqrt{221}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-24)-12\sqrt{221}}{2*42}=\frac{24-12\sqrt{221}}{84} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-24)+12\sqrt{221}}{2*42}=\frac{24+12\sqrt{221}}{84} $
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