12-1/5x=2x+1

Solution for 12-1/5x=2x+1 equation:

12-1/5x=2x+1

We move all terms to the left:

12-1/5x-(2x+1)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R


We get rid of parentheses

-1/5x-2x-1+12=0

We multiply all the terms by the denominator


-2x*5x-1*5x+12*5x-1=0

Wy multiply elements

-10x^2-5x+60x-1=0

We add all the numbers together, and all the variables

-10x^2+55x-1=0

a = -10; b = 55; c = -1;
Δ = b2-4ac
Δ = 552-4·(-10)·(-1)
Δ = 2985
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{-(55)-\sqrt{2985}}{2*-10}=\frac{-55-\sqrt{2985}}{-20}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(55)+\sqrt{2985}}{2*-10}=\frac{-55+\sqrt{2985}}{-20}
$