9x(3x-5)=3*(2x-4)

Solution for 9x(3x-5)=3*(2x-4) equation:

9x(3x-5)=3(2x-4)

We move all terms to the left:

9x(3x-5)-(3(2x-4))=0

We multiply parentheses

27x^2-45x-(3(2x-4))=0


We calculate terms in parentheses: -(3(2x-4)), so:

3(2x-4)

We multiply parentheses

6x-12

Back to the equation:

-(6x-12)


We get rid of parentheses

27x^2-45x-6x+12=0

We add all the numbers together, and all the variables

27x^2-51x+12=0

a = 27; b = -51; c = +12;
Δ = b2-4ac
Δ = -512-4·27·12
Δ = 1305
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:

$\sqrt{\Delta}=\sqrt{1305}=\sqrt{9*145}=\sqrt{9}*\sqrt{145}=3\sqrt{145}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-51)-3\sqrt{145}}{2*27}=\frac{51-3\sqrt{145}}{54}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-51)+3\sqrt{145}}{2*27}=\frac{51+3\sqrt{145}}{54}
$