-8x(x-1)-x-11=-9(x+4)+17

Solution for -8x(x-1)-x-11=-9(x+4)+17 equation:

-8x(x-1)-x-11=-9(x+4)+17

We move all terms to the left:

-8x(x-1)-x-11-(-9(x+4)+17)=0

We add all the numbers together, and all the variables

-1x-8x(x-1)-(-9(x+4)+17)-11=0

We multiply parentheses

-8x^2-1x+8x-(-9(x+4)+17)-11=0


We calculate terms in parentheses: -(-9(x+4)+17), so:

-9(x+4)+17

We multiply parentheses

-9x-36+17

We add all the numbers together, and all the variables

-9x-19

Back to the equation:

-(-9x-19)


We add all the numbers together, and all the variables

-8x^2+7x-(-9x-19)-11=0

We get rid of parentheses

-8x^2+7x+9x+19-11=0

We add all the numbers together, and all the variables

-8x^2+16x+8=0

a = -8; b = 16; c = +8;
Δ = b2-4ac
Δ = 162-4·(-8)·8
Δ = 512
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:

$\sqrt{\Delta}=\sqrt{512}=\sqrt{256*2}=\sqrt{256}*\sqrt{2}=16\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(16)-16\sqrt{2}}{2*-8}=\frac{-16-16\sqrt{2}}{-16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(16)+16\sqrt{2}}{2*-8}=\frac{-16+16\sqrt{2}}{-16}
$