X=(3x-1)(2x-3)

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

X=(3X-1)(2X-3)

We move all terms to the left:

X-((3X-1)(2X-3))=0

We multiply parentheses ..

-((+6X^2-9X-2X+3))+X=0


We calculate terms in parentheses: -((+6X^2-9X-2X+3)), so:

(+6X^2-9X-2X+3)

We get rid of parentheses

6X^2-9X-2X+3

We add all the numbers together, and all the variables

6X^2-11X+3

Back to the equation:

-(6X^2-11X+3)


We add all the numbers together, and all the variables

X-(6X^2-11X+3)=0

We get rid of parentheses

-6X^2+X+11X-3=0

We add all the numbers together, and all the variables

-6X^2+12X-3=0

a = -6; b = 12; c = -3;
Δ = b2-4ac
Δ = 122-4·(-6)·(-3)
Δ = 72
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:

$\sqrt{\Delta}=\sqrt{72}=\sqrt{36*2}=\sqrt{36}*\sqrt{2}=6\sqrt{2}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-6\sqrt{2}}{2*-6}=\frac{-12-6\sqrt{2}}{-12}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+6\sqrt{2}}{2*-6}=\frac{-12+6\sqrt{2}}{-12}
$