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

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

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

We move all terms to the left:

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

We multiply parentheses ..

-((+6X^2-3X+2X-1))+X=0


We calculate terms in parentheses: -((+6X^2-3X+2X-1)), so:

(+6X^2-3X+2X-1)

We get rid of parentheses

6X^2-3X+2X-1

We add all the numbers together, and all the variables

6X^2-1X-1

Back to the equation:

-(6X^2-1X-1)


We add all the numbers together, and all the variables

X-(6X^2-1X-1)=0

We get rid of parentheses

-6X^2+X+1X+1=0

We add all the numbers together, and all the variables

-6X^2+2X+1=0

a = -6; b = 2; c = +1;
Δ = b2-4ac
Δ = 22-4·(-6)·1
Δ = 28
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:

$\sqrt{\Delta}=\sqrt{28}=\sqrt{4*7}=\sqrt{4}*\sqrt{7}=2\sqrt{7}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-2\sqrt{7}}{2*-6}=\frac{-2-2\sqrt{7}}{-12}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2\sqrt{7}}{2*-6}=\frac{-2+2\sqrt{7}}{-12}
$