(2w-1)(5w+7)=0

Solution for (2w-1)(5w+7)=0 equation:

(2w-1)(5w+7)=0

We multiply parentheses ..

(+10w^2+14w-5w-7)=0

We get rid of parentheses

10w^2+14w-5w-7=0

We add all the numbers together, and all the variables

10w^2+9w-7=0

a = 10; b = 9; c = -7;
Δ = b2-4ac
Δ = 92-4·10·(-7)
Δ = 361
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{361}=19$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(9)-19}{2*10}=\frac{-28}{20}
=-1+2/5
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+19}{2*10}=\frac{10}{20}
=1/2
$