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

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

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

We multiply parentheses ..

(+5x^2-25x-8x+40)=0

We get rid of parentheses

5x^2-25x-8x+40=0

We add all the numbers together, and all the variables

5x^2-33x+40=0

a = 5; b = -33; c = +40;
Δ = b2-4ac
Δ = -332-4·5·40
Δ = 289
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{289}=17$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-33)-17}{2*5}=\frac{16}{10}
=1+3/5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-33)+17}{2*5}=\frac{50}{10}
=5
$