(2w-3)(4w-7)=0

Solution for (2w-3)(4w-7)=0 equation:

(2w-3)(4w-7)=0

We multiply parentheses ..

(+8w^2-14w-12w+21)=0

We get rid of parentheses

8w^2-14w-12w+21=0

We add all the numbers together, and all the variables

8w^2-26w+21=0

a = 8; b = -26; c = +21;
Δ = b2-4ac
Δ = -262-4·8·21
Δ = 4
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4}=2$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-26)-2}{2*8}=\frac{24}{16}
=1+1/2
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-26)+2}{2*8}=\frac{28}{16}
=1+3/4
$