4=9x(x+1)

Solution for 4=9x(x+1) equation:

4=9x(x+1)

We move all terms to the left:

4-(9x(x+1))=0


We calculate terms in parentheses: -(9x(x+1)), so:

9x(x+1)

We multiply parentheses

9x^2+9x

Back to the equation:

-(9x^2+9x)


We get rid of parentheses

-9x^2-9x+4=0

a = -9; b = -9; c = +4;
Δ = b2-4ac
Δ = -92-4·(-9)·4
Δ = 225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{225}=15$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-9)-15}{2*-9}=\frac{-6}{-18}
=1/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+15}{2*-9}=\frac{24}{-18}
=-1+1/3
$