6(x-5)4x=3(4x-5)

Solution for 6(x-5)4x=3(4x-5) equation:

6(x-5)4x=3(4x-5)

We move all terms to the left:

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

We multiply parentheses

24x^2-120x-(3(4x-5))=0


We calculate terms in parentheses: -(3(4x-5)), so:

3(4x-5)

We multiply parentheses

12x-15

Back to the equation:

-(12x-15)


We get rid of parentheses

24x^2-120x-12x+15=0

We add all the numbers together, and all the variables

24x^2-132x+15=0

a = 24; b = -132; c = +15;
Δ = b2-4ac
Δ = -1322-4·24·15
Δ = 15984
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{15984}=\sqrt{144*111}=\sqrt{144}*\sqrt{111}=12\sqrt{111}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-132)-12\sqrt{111}}{2*24}=\frac{132-12\sqrt{111}}{48}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-132)+12\sqrt{111}}{2*24}=\frac{132+12\sqrt{111}}{48}
$