1/3.x=2x-45

Solution for 1/3.x=2x-45 equation:

1/3.x=2x-45

We move all terms to the left:

1/3.x-(2x-45)=0


Domain of the equation: 3.x!=0

x!=0/3.

x!=0

x∈R


We get rid of parentheses

1/3.x-2x+45=0

We multiply all the terms by the denominator


-2x*3.x+45*3.x+1=0

Wy multiply elements

-6x^2+135x+1=0

a = -6; b = 135; c = +1;
Δ = b2-4ac
Δ = 1352-4·(-6)·1
Δ = 18249
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{-(135)-\sqrt{18249}}{2*-6}=\frac{-135-\sqrt{18249}}{-12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(135)+\sqrt{18249}}{2*-6}=\frac{-135+\sqrt{18249}}{-12}
$