8(x-9)(x-8)=x+8-(x+5)

Solution for 8(x-9)(x-8)=x+8-(x+5) equation:

8(x-9)(x-8)=x+8-(x+5)

We move all terms to the left:

8(x-9)(x-8)-(x+8-(x+5))=0

We multiply parentheses ..

8(+x^2-8x-9x+72)-(x+8-(x+5))=0


We calculate terms in parentheses: -(x+8-(x+5)), so:

x+8-(x+5)

determiningTheFunctionDomain
x-(x+5)+8

We get rid of parentheses

x-x-5+8

We add all the numbers together, and all the variables

3

Back to the equation:

-(3)


We multiply parentheses

8x^2-64x-72x+576-3=0

We add all the numbers together, and all the variables

8x^2-136x+573=0

a = 8; b = -136; c = +573;
Δ = b2-4ac
Δ = -1362-4·8·573
Δ = 160
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:

$\sqrt{\Delta}=\sqrt{160}=\sqrt{16*10}=\sqrt{16}*\sqrt{10}=4\sqrt{10}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-136)-4\sqrt{10}}{2*8}=\frac{136-4\sqrt{10}}{16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-136)+4\sqrt{10}}{2*8}=\frac{136+4\sqrt{10}}{16}
$