(x)=(2x-1)(4x+7)-12x(-x-1)

Solution for (x)=(2x-1)(4x+7)-12x(-x-1) equation:

(x)=(2x-1)(4x+7)-12x(-x-1)

We move all terms to the left:

(x)-((2x-1)(4x+7)-12x(-x-1))=0

We add all the numbers together, and all the variables

x-((2x-1)(4x+7)-12x(-1x-1))=0

We multiply parentheses ..

-((+8x^2+14x-4x-7)-12x(-1x-1))+x=0


We calculate terms in parentheses: -((+8x^2+14x-4x-7)-12x(-1x-1)), so:

(+8x^2+14x-4x-7)-12x(-1x-1)

We multiply parentheses

(+8x^2+14x-4x-7)+12x^2+12x

We get rid of parentheses

8x^2+12x^2+14x-4x+12x-7

We add all the numbers together, and all the variables

20x^2+22x-7

Back to the equation:

-(20x^2+22x-7)


We add all the numbers together, and all the variables

x-(20x^2+22x-7)=0

We get rid of parentheses

-20x^2+x-22x+7=0

We add all the numbers together, and all the variables

-20x^2-21x+7=0

a = -20; b = -21; c = +7;
Δ = b2-4ac
Δ = -212-4·(-20)·7
Δ = 1001
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-21)-\sqrt{1001}}{2*-20}=\frac{21-\sqrt{1001}}{-40}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-21)+\sqrt{1001}}{2*-20}=\frac{21+\sqrt{1001}}{-40}
$