6x-4x(x-9)=2(3-x)

Solution for 6x-4x(x-9)=2(3-x) equation:

6x-4x(x-9)=2(3-x)

We move all terms to the left:

6x-4x(x-9)-(2(3-x))=0

We add all the numbers together, and all the variables

6x-4x(x-9)-(2(-1x+3))=0

We multiply parentheses

-4x^2+6x+36x-(2(-1x+3))=0


We calculate terms in parentheses: -(2(-1x+3)), so:

2(-1x+3)

We multiply parentheses

-2x+6

Back to the equation:

-(-2x+6)


We add all the numbers together, and all the variables

-4x^2+42x-(-2x+6)=0

We get rid of parentheses

-4x^2+42x+2x-6=0

We add all the numbers together, and all the variables

-4x^2+44x-6=0

a = -4; b = 44; c = -6;
Δ = b2-4ac
Δ = 442-4·(-4)·(-6)
Δ = 1840
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{1840}=\sqrt{16*115}=\sqrt{16}*\sqrt{115}=4\sqrt{115}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(44)-4\sqrt{115}}{2*-4}=\frac{-44-4\sqrt{115}}{-8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(44)+4\sqrt{115}}{2*-4}=\frac{-44+4\sqrt{115}}{-8}
$