40-5x=-8x(x-8)

Solution for 40-5x=-8x(x-8) equation:

40-5x=-8x(x-8)

We move all terms to the left:

40-5x-(-8x(x-8))=0


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

-8x(x-8)

We multiply parentheses

-8x^2+64x

Back to the equation:

-(-8x^2+64x)


We get rid of parentheses

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

We add all the numbers together, and all the variables

8x^2-69x+40=0

a = 8; b = -69; c = +40;
Δ = b2-4ac
Δ = -692-4·8·40
Δ = 3481
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{3481}=59$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-69)-59}{2*8}=\frac{10}{16}
=5/8
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-69)+59}{2*8}=\frac{128}{16}
=8
$