-8w(w+1)=-5(w+10)

Solution for -8w(w+1)=-5(w+10) equation:

-8w(w+1)=-5(w+10)

We move all terms to the left:

-8w(w+1)-(-5(w+10))=0

We multiply parentheses

-8w^2-8w-(-5(w+10))=0


We calculate terms in parentheses: -(-5(w+10)), so:

-5(w+10)

We multiply parentheses

-5w-50

Back to the equation:

-(-5w-50)


We get rid of parentheses

-8w^2-8w+5w+50=0

We add all the numbers together, and all the variables

-8w^2-3w+50=0

a = -8; b = -3; c = +50;
Δ = b2-4ac
Δ = -32-4·(-8)·50
Δ = 1609
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3)-\sqrt{1609}}{2*-8}=\frac{3-\sqrt{1609}}{-16}
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+\sqrt{1609}}{2*-8}=\frac{3+\sqrt{1609}}{-16}
$