2/3x-92x+2=1

Solution for 2/3x-92x+2=1 equation:

2/3x-92x+2=1

We move all terms to the left:

2/3x-92x+2-(1)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We add all the numbers together, and all the variables

-92x+2/3x+1=0

We multiply all the terms by the denominator


-92x*3x+1*3x+2=0

Wy multiply elements

-276x^2+3x+2=0

a = -276; b = 3; c = +2;
Δ = b2-4ac
Δ = 32-4·(-276)·2
Δ = 2217
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{-(3)-\sqrt{2217}}{2*-276}=\frac{-3-\sqrt{2217}}{-552}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+\sqrt{2217}}{2*-276}=\frac{-3+\sqrt{2217}}{-552}
$