3x+25/x+5=6x-237

Solution for 3x+25/x+5=6x-237 equation:

3x+25/x+5=6x-237

We move all terms to the left:

3x+25/x+5-(6x-237)=0


Domain of the equation: x!=0

x∈R


We get rid of parentheses

3x+25/x-6x+237+5=0

We multiply all the terms by the denominator


3x*x-6x*x+237*x+5*x+25=0

We add all the numbers together, and all the variables

242x+3x*x-6x*x+25=0

Wy multiply elements

3x^2-6x^2+242x+25=0

We add all the numbers together, and all the variables

-3x^2+242x+25=0

a = -3; b = 242; c = +25;
Δ = b2-4ac
Δ = 2422-4·(-3)·25
Δ = 58864
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:

$\sqrt{\Delta}=\sqrt{58864}=\sqrt{16*3679}=\sqrt{16}*\sqrt{3679}=4\sqrt{3679}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(242)-4\sqrt{3679}}{2*-3}=\frac{-242-4\sqrt{3679}}{-6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(242)+4\sqrt{3679}}{2*-3}=\frac{-242+4\sqrt{3679}}{-6}
$