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

Solution for 0=(8x+5)(x-8) equation:

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

We move all terms to the left:

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

We add all the numbers together, and all the variables

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

We multiply parentheses ..

-((+8x^2-64x+5x-40))=0


We calculate terms in parentheses: -((+8x^2-64x+5x-40)), so:

(+8x^2-64x+5x-40)

We get rid of parentheses

8x^2-64x+5x-40

We add all the numbers together, and all the variables

8x^2-59x-40

Back to the equation:

-(8x^2-59x-40)


We get rid of parentheses

-8x^2+59x+40=0

a = -8; b = 59; c = +40;
Δ = b2-4ac
Δ = 592-4·(-8)·40
Δ = 4761
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4761}=69$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(59)-69}{2*-8}=\frac{-128}{-16}
=+8
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(59)+69}{2*-8}=\frac{10}{-16}
=-5/8
$