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

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

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

We multiply parentheses ..

(+4x^2-32x-5x+40)=0

We get rid of parentheses

4x^2-32x-5x+40=0

We add all the numbers together, and all the variables

4x^2-37x+40=0

a = 4; b = -37; c = +40;
Δ = b2-4ac
Δ = -372-4·4·40
Δ = 729
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{729}=27$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-37)-27}{2*4}=\frac{10}{8}
=1+1/4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-37)+27}{2*4}=\frac{64}{8}
=8
$