(6x-1)(4x-5)=0

Solution for (6x-1)(4x-5)=0 equation:

(6x-1)(4x-5)=0

We multiply parentheses ..

(+24x^2-30x-4x+5)=0

We get rid of parentheses

24x^2-30x-4x+5=0

We add all the numbers together, and all the variables

24x^2-34x+5=0

a = 24; b = -34; c = +5;
Δ = b2-4ac
Δ = -342-4·24·5
Δ = 676
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{676}=26$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-34)-26}{2*24}=\frac{8}{48}
=1/6
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-34)+26}{2*24}=\frac{60}{48}
=1+1/4
$