4x(3x-1)=5x

Solution for 4x(3x-1)=5x equation:

4x(3x-1)=5x

We move all terms to the left:

4x(3x-1)-(5x)=0

We add all the numbers together, and all the variables

-5x+4x(3x-1)=0

We multiply parentheses

12x^2-5x-4x=0

We add all the numbers together, and all the variables

12x^2-9x=0

a = 12; b = -9; c = 0;
Δ = b2-4ac
Δ = -92-4·12·0
Δ = 81
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{81}=9$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-9)-9}{2*12}=\frac{0}{24}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+9}{2*12}=\frac{18}{24}
=3/4
$