(8x-5)(4x-7)=0

Solution for (8x-5)(4x-7)=0 equation:

(8x-5)(4x-7)=0

We multiply parentheses ..

(+32x^2-56x-20x+35)=0

We get rid of parentheses

32x^2-56x-20x+35=0

We add all the numbers together, and all the variables

32x^2-76x+35=0

a = 32; b = -76; c = +35;
Δ = b2-4ac
Δ = -762-4·32·35
Δ = 1296
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1296}=36$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-76)-36}{2*32}=\frac{40}{64}
=5/8
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-76)+36}{2*32}=\frac{112}{64}
=1+3/4
$