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

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

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

We move all terms to the left:

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

We add all the numbers together, and all the variables

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

We use the square of the difference formula

x^2+11x+2(x-2)2-(3x(x-1)-7)-16=0

We multiply parentheses

x^2+11x+4x-(3x(x-1)-7)-8-16=0


We calculate terms in parentheses: -(3x(x-1)-7), so:

3x(x-1)-7

We multiply parentheses

3x^2-3x-7

Back to the equation:

-(3x^2-3x-7)


We add all the numbers together, and all the variables

x^2+15x-(3x^2-3x-7)-24=0

We get rid of parentheses

x^2-3x^2+15x+3x+7-24=0

We add all the numbers together, and all the variables

-2x^2+18x-17=0

a = -2; b = 18; c = -17;
Δ = b2-4ac
Δ = 182-4·(-2)·(-17)
Δ = 188
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:

$\sqrt{\Delta}=\sqrt{188}=\sqrt{4*47}=\sqrt{4}*\sqrt{47}=2\sqrt{47}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(18)-2\sqrt{47}}{2*-2}=\frac{-18-2\sqrt{47}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(18)+2\sqrt{47}}{2*-2}=\frac{-18+2\sqrt{47}}{-4}
$