(2x+1)(2x+6)-7x(x-2)=4(x+1)(x-1)-9x)

Solution for (2x+1)(2x+6)-7x(x-2)=4(x+1)(x-1)-9x) equation:

(2x+1)(2x+6)-7x(x-2)=4(x+1)(x-1)-9x)

We move all terms to the left:

(2x+1)(2x+6)-7x(x-2)-(4(x+1)(x-1)-9x))=0

We use the square of the difference formula

x^2+(2x+1)(2x+6)-7x(x-2)+1=0

We multiply parentheses

x^2-7x^2+(2x+1)(2x+6)+14x+1=0

We multiply parentheses ..

x^2-7x^2+(+4x^2+12x+2x+6)+14x+1=0

We add all the numbers together, and all the variables

-6x^2+(+4x^2+12x+2x+6)+14x+1=0

We get rid of parentheses

-6x^2+4x^2+12x+2x+14x+6+1=0

We add all the numbers together, and all the variables

-2x^2+28x+7=0

a = -2; b = 28; c = +7;
Δ = b2-4ac
Δ = 282-4·(-2)·7
Δ = 840
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:

$\sqrt{\Delta}=\sqrt{840}=\sqrt{4*210}=\sqrt{4}*\sqrt{210}=2\sqrt{210}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(28)-2\sqrt{210}}{2*-2}=\frac{-28-2\sqrt{210}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(28)+2\sqrt{210}}{2*-2}=\frac{-28+2\sqrt{210}}{-4}
$