x+12=2x-3/5x

Solution for x+12=2x-3/5x equation:

x+12=2x-3/5x

We move all terms to the left:

x+12-(2x-3/5x)=0


Domain of the equation: 5x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

x-(+2x-3/5x)+12=0

We get rid of parentheses

x-2x+3/5x+12=0

We multiply all the terms by the denominator


x*5x-2x*5x+12*5x+3=0

Wy multiply elements

5x^2-10x^2+60x+3=0

We add all the numbers together, and all the variables

-5x^2+60x+3=0

a = -5; b = 60; c = +3;
Δ = b2-4ac
Δ = 602-4·(-5)·3
Δ = 3660
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:

$\sqrt{\Delta}=\sqrt{3660}=\sqrt{4*915}=\sqrt{4}*\sqrt{915}=2\sqrt{915}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(60)-2\sqrt{915}}{2*-5}=\frac{-60-2\sqrt{915}}{-10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(60)+2\sqrt{915}}{2*-5}=\frac{-60+2\sqrt{915}}{-10}
$