4x(6x+3)=21

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Solution for 4x(6x+3)=21 equation:



4x(6x+3)=21
We move all terms to the left:
4x(6x+3)-(21)=0
We multiply parentheses
24x^2+12x-21=0
a = 24; b = 12; c = -21;
Δ = b2-4ac
Δ = 122-4·24·(-21)
Δ = 2160
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:
$\sqrt{\Delta}=\sqrt{2160}=\sqrt{144*15}=\sqrt{144}*\sqrt{15}=12\sqrt{15}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-12\sqrt{15}}{2*24}=\frac{-12-12\sqrt{15}}{48} $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+12\sqrt{15}}{2*24}=\frac{-12+12\sqrt{15}}{48} $

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