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6x(12x+7)=83
We move all terms to the left:
6x(12x+7)-(83)=0
We multiply parentheses
72x^2+42x-83=0
a = 72; b = 42; c = -83;
Δ = b2-4ac
Δ = 422-4·72·(-83)
Δ = 25668
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{25668}=\sqrt{36*713}=\sqrt{36}*\sqrt{713}=6\sqrt{713}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(42)-6\sqrt{713}}{2*72}=\frac{-42-6\sqrt{713}}{144} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(42)+6\sqrt{713}}{2*72}=\frac{-42+6\sqrt{713}}{144} $
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