15/(x-5)=5x

Solution for 15/(x-5)=5x equation:

15/(x-5)=5x

We move all terms to the left:

15/(x-5)-(5x)=0


Domain of the equation: (x-5)!=0

We move all terms containing x to the left, all other terms to the right

x!=5

x∈R


We add all the numbers together, and all the variables

-5x+15/(x-5)=0

We multiply all the terms by the denominator


-5x*(x-5)+15=0

We multiply parentheses

-5x^2+25x+15=0

a = -5; b = 25; c = +15;
Δ = b2-4ac
Δ = 252-4·(-5)·15
Δ = 925
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:

$\sqrt{\Delta}=\sqrt{925}=\sqrt{25*37}=\sqrt{25}*\sqrt{37}=5\sqrt{37}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(25)-5\sqrt{37}}{2*-5}=\frac{-25-5\sqrt{37}}{-10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(25)+5\sqrt{37}}{2*-5}=\frac{-25+5\sqrt{37}}{-10}
$