10/3x+60=5x

Solution for 10/3x+60=5x equation:

10/3x+60=5x

We move all terms to the left:

10/3x+60-(5x)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We add all the numbers together, and all the variables

-5x+10/3x+60=0

We multiply all the terms by the denominator


-5x*3x+60*3x+10=0

Wy multiply elements

-15x^2+180x+10=0

a = -15; b = 180; c = +10;
Δ = b2-4ac
Δ = 1802-4·(-15)·10
Δ = 33000
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:

$\sqrt{\Delta}=\sqrt{33000}=\sqrt{100*330}=\sqrt{100}*\sqrt{330}=10\sqrt{330}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(180)-10\sqrt{330}}{2*-15}=\frac{-180-10\sqrt{330}}{-30}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(180)+10\sqrt{330}}{2*-15}=\frac{-180+10\sqrt{330}}{-30}
$