12x-9=(2x+1)(4x-3)

Solution for 12x-9=(2x+1)(4x-3) equation:

12x-9=(2x+1)(4x-3)

We move all terms to the left:

12x-9-((2x+1)(4x-3))=0

We multiply parentheses ..

-((+8x^2-6x+4x-3))+12x-9=0


We calculate terms in parentheses: -((+8x^2-6x+4x-3)), so:

(+8x^2-6x+4x-3)

We get rid of parentheses

8x^2-6x+4x-3

We add all the numbers together, and all the variables

8x^2-2x-3

Back to the equation:

-(8x^2-2x-3)


We add all the numbers together, and all the variables

12x-(8x^2-2x-3)-9=0

We get rid of parentheses

-8x^2+12x+2x+3-9=0

We add all the numbers together, and all the variables

-8x^2+14x-6=0

a = -8; b = 14; c = -6;
Δ = b2-4ac
Δ = 142-4·(-8)·(-6)
Δ = 4
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4}=2$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(14)-2}{2*-8}=\frac{-16}{-16}
=1
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(14)+2}{2*-8}=\frac{-12}{-16}
=3/4
$