4(-4x^2-8x+1)=-11(1+2x+x^2)

Solution for 4(-4x^2-8x+1)=-11(1+2x+x^2) equation:

4(-4x^2-8x+1)=-11(1+2x+x^2)

We move all terms to the left:

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

We multiply parentheses

-16x^2-(-11(1+2x+x^2))-32x+4=0


We calculate terms in parentheses: -(-11(1+2x+x^2)), so:

-11(1+2x+x^2)

We multiply parentheses

-11x^2-22x-11

Back to the equation:

-(-11x^2-22x-11)


We get rid of parentheses

-16x^2+11x^2+22x-32x+11+4=0

We add all the numbers together, and all the variables

-5x^2-10x+15=0

a = -5; b = -10; c = +15;
Δ = b2-4ac
Δ = -102-4·(-5)·15
Δ = 400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{400}=20$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-20}{2*-5}=\frac{-10}{-10}
=1
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+20}{2*-5}=\frac{30}{-10}
=-3
$