x=(-4x+6)(x-3)

Solution for x=(-4x+6)(x-3) equation:

x=(-4x+6)(x-3)

We move all terms to the left:

x-((-4x+6)(x-3))=0

We multiply parentheses ..

-((-4x^2+12x+6x-18))+x=0


We calculate terms in parentheses: -((-4x^2+12x+6x-18)), so:

(-4x^2+12x+6x-18)

We get rid of parentheses

-4x^2+12x+6x-18

We add all the numbers together, and all the variables

-4x^2+18x-18

Back to the equation:

-(-4x^2+18x-18)


We get rid of parentheses

4x^2-18x+x+18=0

We add all the numbers together, and all the variables

4x^2-17x+18=0

a = 4; b = -17; c = +18;
Δ = b2-4ac
Δ = -172-4·4·18
Δ = 1
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1}=1$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-17)-1}{2*4}=\frac{16}{8}
=2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-17)+1}{2*4}=\frac{18}{8}
=2+1/4
$