10/(x+2)=15x

Solution for 10/(x+2)=15x equation:

10/(x+2)=15x

We move all terms to the left:

10/(x+2)-(15x)=0


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

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

x!=-2

x∈R


We add all the numbers together, and all the variables

-15x+10/(x+2)=0

We multiply all the terms by the denominator


-15x*(x+2)+10=0

We multiply parentheses

-15x^2-30x+10=0

a = -15; b = -30; c = +10;
Δ = b2-4ac
Δ = -302-4·(-15)·10
Δ = 1500
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:

$\sqrt{\Delta}=\sqrt{1500}=\sqrt{100*15}=\sqrt{100}*\sqrt{15}=10\sqrt{15}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-30)-10\sqrt{15}}{2*-15}=\frac{30-10\sqrt{15}}{-30}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-30)+10\sqrt{15}}{2*-15}=\frac{30+10\sqrt{15}}{-30}
$