5/3x-x+1=-12/6

Solution for 5/3x-x+1=-12/6 equation:

5/3x-x+1=-12/6

We move all terms to the left:

5/3x-x+1-(-12/6)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We add all the numbers together, and all the variables

5/3x-x+1-(-2)=0

We add all the numbers together, and all the variables

-1x+5/3x+3=0

We multiply all the terms by the denominator


-1x*3x+3*3x+5=0

Wy multiply elements

-3x^2+9x+5=0

a = -3; b = 9; c = +5;
Δ = b2-4ac
Δ = 92-4·(-3)·5
Δ = 141
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{-(9)-\sqrt{141}}{2*-3}=\frac{-9-\sqrt{141}}{-6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+\sqrt{141}}{2*-3}=\frac{-9+\sqrt{141}}{-6}
$