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

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

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

We multiply parentheses ..

(+3x^2-8x-15x+40)=0

We get rid of parentheses

3x^2-8x-15x+40=0

We add all the numbers together, and all the variables

3x^2-23x+40=0

a = 3; b = -23; c = +40;
Δ = b2-4ac
Δ = -232-4·3·40
Δ = 49
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{49}=7$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-23)-7}{2*3}=\frac{16}{6}
=2+2/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-23)+7}{2*3}=\frac{30}{6}
=5
$