1/3X-2x=5

Solution for 1/3X-2x=5 equation:

1/3X-2X=5

We move all terms to the left:

1/3X-2X-(5)=0


Domain of the equation: 3X!=0

X!=0/3

X!=0

X∈R


We add all the numbers together, and all the variables

-2X+1/3X-5=0

We multiply all the terms by the denominator


-2X*3X-5*3X+1=0

Wy multiply elements

-6X^2-15X+1=0

a = -6; b = -15; c = +1;
Δ = b2-4ac
Δ = -152-4·(-6)·1
Δ = 249
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{-(-15)-\sqrt{249}}{2*-6}=\frac{15-\sqrt{249}}{-12}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-15)+\sqrt{249}}{2*-6}=\frac{15+\sqrt{249}}{-12}
$