X(x+9)=6x^2

Solution for X(x+9)=6x^2 equation:

X(X+9)=6X^2

We move all terms to the left:

X(X+9)-(6X^2)=0

determiningTheFunctionDomain
-6X^2+X(X+9)=0

We multiply parentheses

-6X^2+X^2+9X=0

We add all the numbers together, and all the variables

-5X^2+9X=0

a = -5; b = 9; c = 0;
Δ = b2-4ac
Δ = 92-4·(-5)·0
Δ = 81
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{81}=9$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(9)-9}{2*-5}=\frac{-18}{-10}
=1+4/5
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+9}{2*-5}=\frac{0}{-10}
=0
$