(5x-8)(3x-16)=0

Solution for (5x-8)(3x-16)=0 equation:

(5x-8)(3x-16)=0

We multiply parentheses ..

(+15x^2-80x-24x+128)=0

We get rid of parentheses

15x^2-80x-24x+128=0

We add all the numbers together, and all the variables

15x^2-104x+128=0

a = 15; b = -104; c = +128;
Δ = b2-4ac
Δ = -1042-4·15·128
Δ = 3136
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{3136}=56$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-104)-56}{2*15}=\frac{48}{30}
=1+3/5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-104)+56}{2*15}=\frac{160}{30}
=5+1/3
$