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4x(6x-3)=24
We move all terms to the left:
4x(6x-3)-(24)=0
We multiply parentheses
24x^2-12x-24=0
a = 24; b = -12; c = -24;
Δ = b2-4ac
Δ = -122-4·24·(-24)
Δ = 2448
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{2448}=\sqrt{144*17}=\sqrt{144}*\sqrt{17}=12\sqrt{17}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-12\sqrt{17}}{2*24}=\frac{12-12\sqrt{17}}{48} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+12\sqrt{17}}{2*24}=\frac{12+12\sqrt{17}}{48} $
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