4x(6x-5)=0

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

4x(6x-5)=0

We multiply parentheses

24x^2-20x=0

a = 24; b = -20; c = 0;
Δ = b2-4ac
Δ = -202-4·24·0
Δ = 400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{400}=20$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-20)-20}{2*24}=\frac{0}{48}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-20)+20}{2*24}=\frac{40}{48}
=5/6
$