(-8w+9)(-5w+7)=0

Solution for (-8w+9)(-5w+7)=0 equation:

(-8w+9)(-5w+7)=0

We multiply parentheses ..

(+40w^2-56w-45w+63)=0

We get rid of parentheses

40w^2-56w-45w+63=0

We add all the numbers together, and all the variables

40w^2-101w+63=0

a = 40; b = -101; c = +63;
Δ = b2-4ac
Δ = -1012-4·40·63
Δ = 121
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{121}=11$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-101)-11}{2*40}=\frac{90}{80}
=1+1/8
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-101)+11}{2*40}=\frac{112}{80}
=1+2/5
$