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

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

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

We multiply parentheses

5x^2-8x-15x+24=0

We add all the numbers together, and all the variables

5x^2-23x+24=0

a = 5; b = -23; c = +24;
Δ = b2-4ac
Δ = -232-4·5·24
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*5}=\frac{16}{10}
=1+3/5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-23)+7}{2*5}=\frac{30}{10}
=3
$