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

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

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

We move all terms to the left:

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

We multiply parentheses

24x^2-4x-(5(5x-1))=0


We calculate terms in parentheses: -(5(5x-1)), so:

5(5x-1)

We multiply parentheses

25x-5

Back to the equation:

-(25x-5)


We get rid of parentheses

24x^2-4x-25x+5=0

We add all the numbers together, and all the variables

24x^2-29x+5=0

a = 24; b = -29; c = +5;
Δ = b2-4ac
Δ = -292-4·24·5
Δ = 361
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{361}=19$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-29)-19}{2*24}=\frac{10}{48}
=5/24
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-29)+19}{2*24}=\frac{48}{48}
=1
$