-9x(x+1)=-3x-21

Solution for -9x(x+1)=-3x-21 equation:

-9x(x+1)=-3x-21

We move all terms to the left:

-9x(x+1)-(-3x-21)=0

We multiply parentheses

-9x^2-9x-(-3x-21)=0

We get rid of parentheses

-9x^2-9x+3x+21=0

We add all the numbers together, and all the variables

-9x^2-6x+21=0

a = -9; b = -6; c = +21;
Δ = b2-4ac
Δ = -62-4·(-9)·21
Δ = 792
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:

$\sqrt{\Delta}=\sqrt{792}=\sqrt{36*22}=\sqrt{36}*\sqrt{22}=6\sqrt{22}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-6\sqrt{22}}{2*-9}=\frac{6-6\sqrt{22}}{-18}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+6\sqrt{22}}{2*-9}=\frac{6+6\sqrt{22}}{-18}
$