3(2x-1)=9(3x-5)x=

Solution for 3(2x-1)=9(3x-5)x= equation:

3(2x-1)=9(3x-5)x=

We move all terms to the left:

3(2x-1)-(9(3x-5)x)=0

We multiply parentheses

6x-(9(3x-5)x)-3=0


We calculate terms in parentheses: -(9(3x-5)x), so:

9(3x-5)x

We multiply parentheses

27x^2-45x

Back to the equation:

-(27x^2-45x)


We get rid of parentheses

-27x^2+6x+45x-3=0

We add all the numbers together, and all the variables

-27x^2+51x-3=0

a = -27; b = 51; c = -3;
Δ = b2-4ac
Δ = 512-4·(-27)·(-3)
Δ = 2277
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:

$\sqrt{\Delta}=\sqrt{2277}=\sqrt{9*253}=\sqrt{9}*\sqrt{253}=3\sqrt{253}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(51)-3\sqrt{253}}{2*-27}=\frac{-51-3\sqrt{253}}{-54}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(51)+3\sqrt{253}}{2*-27}=\frac{-51+3\sqrt{253}}{-54}
$