30x/5x+6x=10/5x

Solution for 30x/5x+6x=10/5x equation:

30x/5x+6x=10/5x

We move all terms to the left:

30x/5x+6x-(10/5x)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R



Domain of the equation: 5x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

30x/5x+6x-(+10/5x)=0

We add all the numbers together, and all the variables

6x+30x/5x-(+10/5x)=0

We get rid of parentheses

6x+30x/5x-10/5x=0

We multiply all the terms by the denominator


6x*5x+30x-10=0

We add all the numbers together, and all the variables

30x+6x*5x-10=0

Wy multiply elements

30x^2+30x-10=0

a = 30; b = 30; c = -10;
Δ = b2-4ac
Δ = 302-4·30·(-10)
Δ = 2100
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:

$\sqrt{\Delta}=\sqrt{2100}=\sqrt{100*21}=\sqrt{100}*\sqrt{21}=10\sqrt{21}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(30)-10\sqrt{21}}{2*30}=\frac{-30-10\sqrt{21}}{60}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(30)+10\sqrt{21}}{2*30}=\frac{-30+10\sqrt{21}}{60}
$