8(x-9)(x-8)=x+8(x-3)

Solution for 8(x-9)(x-8)=x+8(x-3) equation:

8(x-9)(x-8)=x+8(x-3)

We move all terms to the left:

8(x-9)(x-8)-(x+8(x-3))=0

We multiply parentheses ..

8(+x^2-8x-9x+72)-(x+8(x-3))=0


We calculate terms in parentheses: -(x+8(x-3)), so:

x+8(x-3)

We multiply parentheses

x+8x-24

We add all the numbers together, and all the variables

9x-24

Back to the equation:

-(9x-24)


We multiply parentheses

8x^2-64x-72x-(9x-24)+576=0

We get rid of parentheses

8x^2-64x-72x-9x+24+576=0

We add all the numbers together, and all the variables

8x^2-145x+600=0

a = 8; b = -145; c = +600;
Δ = b2-4ac
Δ = -1452-4·8·600
Δ = 1825
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:

$\sqrt{\Delta}=\sqrt{1825}=\sqrt{25*73}=\sqrt{25}*\sqrt{73}=5\sqrt{73}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-145)-5\sqrt{73}}{2*8}=\frac{145-5\sqrt{73}}{16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-145)+5\sqrt{73}}{2*8}=\frac{145+5\sqrt{73}}{16}
$