X=9-12x+4x^2

Solution for X=9-12x+4x^2 equation:

X=9-12X+4X^2

We move all terms to the left:

X-(9-12X+4X^2)=0

We get rid of parentheses

-4X^2+12X+X-9=0

We add all the numbers together, and all the variables

-4X^2+13X-9=0

a = -4; b = 13; c = -9;
Δ = b2-4ac
Δ = 132-4·(-4)·(-9)
Δ = 25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{25}=5$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(13)-5}{2*-4}=\frac{-18}{-8}
=2+1/4
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(13)+5}{2*-4}=\frac{-8}{-8}
=1
$