3x(x+8)=21

Solution for 3x(x+8)=21 equation:

3x(x+8)=21

We move all terms to the left:

3x(x+8)-(21)=0

We multiply parentheses

3x^2+24x-21=0

a = 3; b = 24; c = -21;
Δ = b2-4ac
Δ = 242-4·3·(-21)
Δ = 828
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:

$\sqrt{\Delta}=\sqrt{828}=\sqrt{36*23}=\sqrt{36}*\sqrt{23}=6\sqrt{23}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(24)-6\sqrt{23}}{2*3}=\frac{-24-6\sqrt{23}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(24)+6\sqrt{23}}{2*3}=\frac{-24+6\sqrt{23}}{6}
$