2x+12=2/5x

Solution for 2x+12=2/5x equation:

2x+12=2/5x

We move all terms to the left:

2x+12-(2/5x)=0


Domain of the equation: 5x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

2x-(+2/5x)+12=0

We get rid of parentheses

2x-2/5x+12=0

We multiply all the terms by the denominator


2x*5x+12*5x-2=0

Wy multiply elements

10x^2+60x-2=0

a = 10; b = 60; c = -2;
Δ = b2-4ac
Δ = 602-4·10·(-2)
Δ = 3680
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:

$\sqrt{\Delta}=\sqrt{3680}=\sqrt{16*230}=\sqrt{16}*\sqrt{230}=4\sqrt{230}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(60)-4\sqrt{230}}{2*10}=\frac{-60-4\sqrt{230}}{20}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(60)+4\sqrt{230}}{2*10}=\frac{-60+4\sqrt{230}}{20}
$