1/(2x+10)=-4x/(8x)

Solution for 1/(2x+10)=-4x/(8x) equation:

1/(2x+10)=-4x/(8x)

We move all terms to the left:

1/(2x+10)-(-4x/(8x))=0


Domain of the equation: (2x+10)!=0

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

2x!=-10

x!=-10/2

x!=-5

x∈R



Domain of the equation: 8x)!=0

x!=0/1

x!=0

x∈R


We get rid of parentheses

1/(2x+10)+4x/8x=0

We calculate fractions


8x/(16x^2+80x)+(8x^2+40x)/(16x^2+80x)=0

We multiply all the terms by the denominator


8x+(8x^2+40x)=0

We get rid of parentheses

8x^2+8x+40x=0

We add all the numbers together, and all the variables

8x^2+48x=0

a = 8; b = 48; c = 0;
Δ = b2-4ac
Δ = 482-4·8·0
Δ = 2304
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2304}=48$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(48)-48}{2*8}=\frac{-96}{16}
=-6
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(48)+48}{2*8}=\frac{0}{16}
=0
$