6/5x=30+x

Solution for 6/5x=30+x equation:

6/5x=30+x

We move all terms to the left:

6/5x-(30+x)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R


We add all the numbers together, and all the variables

6/5x-(x+30)=0

We get rid of parentheses

6/5x-x-30=0

We multiply all the terms by the denominator


-x*5x-30*5x+6=0

Wy multiply elements

-5x^2-150x+6=0

a = -5; b = -150; c = +6;
Δ = b2-4ac
Δ = -1502-4·(-5)·6
Δ = 22620
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:

$\sqrt{\Delta}=\sqrt{22620}=\sqrt{4*5655}=\sqrt{4}*\sqrt{5655}=2\sqrt{5655}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-150)-2\sqrt{5655}}{2*-5}=\frac{150-2\sqrt{5655}}{-10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-150)+2\sqrt{5655}}{2*-5}=\frac{150+2\sqrt{5655}}{-10}
$