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12x(24x+7)=37
We move all terms to the left:
12x(24x+7)-(37)=0
We multiply parentheses
288x^2+84x-37=0
a = 288; b = 84; c = -37;
Δ = b2-4ac
Δ = 842-4·288·(-37)
Δ = 49680
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{49680}=\sqrt{144*345}=\sqrt{144}*\sqrt{345}=12\sqrt{345}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(84)-12\sqrt{345}}{2*288}=\frac{-84-12\sqrt{345}}{576} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(84)+12\sqrt{345}}{2*288}=\frac{-84+12\sqrt{345}}{576} $
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