6x-30=60/4x

Solution for 6x-30=60/4x equation:

6x-30=60/4x

We move all terms to the left:

6x-30-(60/4x)=0


Domain of the equation: 4x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

6x-(+60/4x)-30=0

We get rid of parentheses

6x-60/4x-30=0

We multiply all the terms by the denominator


6x*4x-30*4x-60=0

Wy multiply elements

24x^2-120x-60=0

a = 24; b = -120; c = -60;
Δ = b2-4ac
Δ = -1202-4·24·(-60)
Δ = 20160
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:

$\sqrt{\Delta}=\sqrt{20160}=\sqrt{576*35}=\sqrt{576}*\sqrt{35}=24\sqrt{35}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-120)-24\sqrt{35}}{2*24}=\frac{120-24\sqrt{35}}{48}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-120)+24\sqrt{35}}{2*24}=\frac{120+24\sqrt{35}}{48}
$