((6)/(2x+6))-((5x)/(x+5))=0

Solution for ((6)/(2x+6))-((5x)/(x+5))=0 equation:

((6)/(2x+6))-((5x)/(x+5))=0


Domain of the equation: (2x+6))!=0

x∈R



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

x∈R


We calculate fractions


(-10x^2-30x)/((2x+6))*x+(6x+30)/((2x+6))*x=0

We multiply all the terms by the denominator


(-10x^2-30x)+(6x+30)=0

We get rid of parentheses

-10x^2-30x+6x+30=0

We add all the numbers together, and all the variables

-10x^2-24x+30=0

a = -10; b = -24; c = +30;
Δ = b2-4ac
Δ = -242-4·(-10)·30
Δ = 1776
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:

$\sqrt{\Delta}=\sqrt{1776}=\sqrt{16*111}=\sqrt{16}*\sqrt{111}=4\sqrt{111}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-24)-4\sqrt{111}}{2*-10}=\frac{24-4\sqrt{111}}{-20}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-24)+4\sqrt{111}}{2*-10}=\frac{24+4\sqrt{111}}{-20}
$