30/x=25x+x

Solution for 30/x=25x+x equation:

30/x=25x+x

We move all terms to the left:

30/x-(25x+x)=0


Domain of the equation: x!=0

x∈R


We add all the numbers together, and all the variables

30/x-(+26x)=0

We get rid of parentheses

30/x-26x=0

We multiply all the terms by the denominator


-26x*x+30=0

Wy multiply elements

-26x^2+30=0

a = -26; b = 0; c = +30;
Δ = b2-4ac
Δ = 02-4·(-26)·30
Δ = 3120
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:

$\sqrt{\Delta}=\sqrt{3120}=\sqrt{16*195}=\sqrt{16}*\sqrt{195}=4\sqrt{195}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{195}}{2*-26}=\frac{0-4\sqrt{195}}{-52}
=-\frac{4\sqrt{195}}{-52}
=-\frac{\sqrt{195}}{-13}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{195}}{2*-26}=\frac{0+4\sqrt{195}}{-52}
=\frac{4\sqrt{195}}{-52}
=\frac{\sqrt{195}}{-13}
$