13w-43=8w(w-4)

Solution for 13w-43=8w(w-4) equation:

13w-43=8w(w-4)

We move all terms to the left:

13w-43-(8w(w-4))=0


We calculate terms in parentheses: -(8w(w-4)), so:

8w(w-4)

We multiply parentheses

8w^2-32w

Back to the equation:

-(8w^2-32w)


We get rid of parentheses

-8w^2+13w+32w-43=0

We add all the numbers together, and all the variables

-8w^2+45w-43=0

a = -8; b = 45; c = -43;
Δ = b2-4ac
Δ = 452-4·(-8)·(-43)
Δ = 649
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{-(45)-\sqrt{649}}{2*-8}=\frac{-45-\sqrt{649}}{-16}
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(45)+\sqrt{649}}{2*-8}=\frac{-45+\sqrt{649}}{-16}
$