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

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

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

We move all terms to the left:

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


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

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

x!=-10

x∈R


We get rid of parentheses

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

We multiply all the terms by the denominator


-2x*(x+10)+4*(x+10)+2=0

We multiply parentheses

-2x^2-20x+4x+40+2=0

We add all the numbers together, and all the variables

-2x^2-16x+42=0

a = -2; b = -16; c = +42;
Δ = b2-4ac
Δ = -162-4·(-2)·42
Δ = 592
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:

$\sqrt{\Delta}=\sqrt{592}=\sqrt{16*37}=\sqrt{16}*\sqrt{37}=4\sqrt{37}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-16)-4\sqrt{37}}{2*-2}=\frac{16-4\sqrt{37}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-16)+4\sqrt{37}}{2*-2}=\frac{16+4\sqrt{37}}{-4}
$