3x+9=36x*x+144x+108

Solution for 3x+9=36x*x+144x+108 equation:

3x+9=36x*x+144x+108

We move all terms to the left:

3x+9-(36x*x+144x+108)=0

We add all the numbers together, and all the variables

3x-(144x+36x*x+108)+9=0

We get rid of parentheses

3x-144x-36x*x-108+9=0

We add all the numbers together, and all the variables

-141x-36x*x-99=0

Wy multiply elements

-36x^2-141x-99=0

a = -36; b = -141; c = -99;
Δ = b2-4ac
Δ = -1412-4·(-36)·(-99)
Δ = 5625
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{5625}=75$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-141)-75}{2*-36}=\frac{66}{-72}
=-11/12
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-141)+75}{2*-36}=\frac{216}{-72}
=-3
$