1/(25+15x)=3x+5

Solution for 1/(25+15x)=3x+5 equation:

1/(25+15x)=3x+5

We move all terms to the left:

1/(25+15x)-(3x+5)=0


Domain of the equation: (25+15x)!=0

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

15x!=-25

x!=-25/15

x!=-1+2/3

x∈R


We add all the numbers together, and all the variables

1/(15x+25)-(3x+5)=0

We get rid of parentheses

1/(15x+25)-3x-5=0

We multiply all the terms by the denominator


-3x*(15x+25)-5*(15x+25)+1=0

We multiply parentheses

-45x^2-75x-75x-125+1=0

We add all the numbers together, and all the variables

-45x^2-150x-124=0

a = -45; b = -150; c = -124;
Δ = b2-4ac
Δ = -1502-4·(-45)·(-124)
Δ = 180
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:

$\sqrt{\Delta}=\sqrt{180}=\sqrt{36*5}=\sqrt{36}*\sqrt{5}=6\sqrt{5}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-150)-6\sqrt{5}}{2*-45}=\frac{150-6\sqrt{5}}{-90}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-150)+6\sqrt{5}}{2*-45}=\frac{150+6\sqrt{5}}{-90}
$