-3x(x-4)=-9(x-1)

Solution for -3x(x-4)=-9(x-1) equation:

-3x(x-4)=-9(x-1)

We move all terms to the left:

-3x(x-4)-(-9(x-1))=0

We multiply parentheses

-3x^2+12x-(-9(x-1))=0


We calculate terms in parentheses: -(-9(x-1)), so:

-9(x-1)

We multiply parentheses

-9x+9

Back to the equation:

-(-9x+9)


We get rid of parentheses

-3x^2+12x+9x-9=0

We add all the numbers together, and all the variables

-3x^2+21x-9=0

a = -3; b = 21; c = -9;
Δ = b2-4ac
Δ = 212-4·(-3)·(-9)
Δ = 333
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:

$\sqrt{\Delta}=\sqrt{333}=\sqrt{9*37}=\sqrt{9}*\sqrt{37}=3\sqrt{37}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(21)-3\sqrt{37}}{2*-3}=\frac{-21-3\sqrt{37}}{-6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(21)+3\sqrt{37}}{2*-3}=\frac{-21+3\sqrt{37}}{-6}
$