3(x+3)8x=21

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

3(x+3)8x=21

We move all terms to the left:

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

We multiply parentheses

24x^2+72x-21=0

a = 24; b = 72; c = -21;
Δ = b2-4ac
Δ = 722-4·24·(-21)
Δ = 7200
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:

$\sqrt{\Delta}=\sqrt{7200}=\sqrt{3600*2}=\sqrt{3600}*\sqrt{2}=60\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(72)-60\sqrt{2}}{2*24}=\frac{-72-60\sqrt{2}}{48}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(72)+60\sqrt{2}}{2*24}=\frac{-72+60\sqrt{2}}{48}
$