(x+1)(x-2)-(4-1)(3x+5)-6=8x-11(x-3)(x+7)

Solution for (x+1)(x-2)-(4-1)(3x+5)-6=8x-11(x-3)(x+7) equation:

(x+1)(x-2)-(4-1)(3x+5)-6=8x-11(x-3)(x+7)

We move all terms to the left:

(x+1)(x-2)-(4-1)(3x+5)-6-(8x-11(x-3)(x+7))=0

We add all the numbers together, and all the variables

(x+1)(x-2)-3(3x+5)-(8x-11(x-3)(x+7))-6=0

We multiply parentheses

(x+1)(x-2)-9x-(8x-11(x-3)(x+7))-15-6=0

We multiply parentheses ..

(+x^2-2x+x-2)-9x-(8x-11(x-3)(x+7))-15-6=0


We calculate terms in parentheses: -(8x-11(x-3)(x+7)), so:

8x-11(x-3)(x+7)

We multiply parentheses ..

-11(+x^2+7x-3x-21)+8x

We multiply parentheses

-11x^2-77x+33x+8x+231

We add all the numbers together, and all the variables

-11x^2-36x+231

Back to the equation:

-(-11x^2-36x+231)


We add all the numbers together, and all the variables

(+x^2-2x+x-2)-(-11x^2-36x+231)-9x-21=0

We get rid of parentheses

x^2+11x^2-2x+x+36x-9x-2-231-21=0

We add all the numbers together, and all the variables

12x^2+26x-254=0

a = 12; b = 26; c = -254;
Δ = b2-4ac
Δ = 262-4·12·(-254)
Δ = 12868
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:

$\sqrt{\Delta}=\sqrt{12868}=\sqrt{4*3217}=\sqrt{4}*\sqrt{3217}=2\sqrt{3217}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(26)-2\sqrt{3217}}{2*12}=\frac{-26-2\sqrt{3217}}{24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(26)+2\sqrt{3217}}{2*12}=\frac{-26+2\sqrt{3217}}{24}
$