4x(6x+3)=21

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}
$