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

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

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

We move all terms to the left:

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


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We get rid of parentheses

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

We multiply all the terms by the denominator


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

Wy multiply elements

6x^2-36x^2+15x+6x+5=0

We add all the numbers together, and all the variables

-30x^2+21x+5=0

a = -30; b = 21; c = +5;
Δ = b2-4ac
Δ = 212-4·(-30)·5
Δ = 1041
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(21)-\sqrt{1041}}{2*-30}=\frac{-21-\sqrt{1041}}{-60}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(21)+\sqrt{1041}}{2*-30}=\frac{-21+\sqrt{1041}}{-60}
$