x(21+9x)=8

Solution for x(21+9x)=8 equation:

x(21+9x)=8

We move all terms to the left:

x(21+9x)-(8)=0

We add all the numbers together, and all the variables

x(9x+21)-8=0

We multiply parentheses

9x^2+21x-8=0

a = 9; b = 21; c = -8;
Δ = b2-4ac
Δ = 212-4·9·(-8)
Δ = 729
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{729}=27$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(21)-27}{2*9}=\frac{-48}{18}
=-2+2/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(21)+27}{2*9}=\frac{6}{18}
=1/3
$