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12x(4x+23)=612
We move all terms to the left:
12x(4x+23)-(612)=0
We multiply parentheses
48x^2+276x-612=0
a = 48; b = 276; c = -612;
Δ = b2-4ac
Δ = 2762-4·48·(-612)
Δ = 193680
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{193680}=\sqrt{144*1345}=\sqrt{144}*\sqrt{1345}=12\sqrt{1345}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(276)-12\sqrt{1345}}{2*48}=\frac{-276-12\sqrt{1345}}{96} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(276)+12\sqrt{1345}}{2*48}=\frac{-276+12\sqrt{1345}}{96} $
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