4(3x-5)2x=2(7x-10)

Solution for 4(3x-5)2x=2(7x-10) equation:

4(3x-5)2x=2(7x-10)

We move all terms to the left:

4(3x-5)2x-(2(7x-10))=0

We multiply parentheses

24x^2-40x-(2(7x-10))=0


We calculate terms in parentheses: -(2(7x-10)), so:

2(7x-10)

We multiply parentheses

14x-20

Back to the equation:

-(14x-20)


We get rid of parentheses

24x^2-40x-14x+20=0

We add all the numbers together, and all the variables

24x^2-54x+20=0

a = 24; b = -54; c = +20;
Δ = b2-4ac
Δ = -542-4·24·20
Δ = 996
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:

$\sqrt{\Delta}=\sqrt{996}=\sqrt{4*249}=\sqrt{4}*\sqrt{249}=2\sqrt{249}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-54)-2\sqrt{249}}{2*24}=\frac{54-2\sqrt{249}}{48}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-54)+2\sqrt{249}}{2*24}=\frac{54+2\sqrt{249}}{48}
$