4x(x+9)=x+9

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

4x(x+9)=x+9

We move all terms to the left:

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

We multiply parentheses

4x^2+36x-(x+9)=0

We get rid of parentheses

4x^2+36x-x-9=0

We add all the numbers together, and all the variables

4x^2+35x-9=0

a = 4; b = 35; c = -9;
Δ = b2-4ac
Δ = 352-4·4·(-9)
Δ = 1369
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1369}=37$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(35)-37}{2*4}=\frac{-72}{8}
=-9
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(35)+37}{2*4}=\frac{2}{8}
=1/4
$