131/2x-21x=23

Solution for 131/2x-21x=23 equation:

131/2x-21x=23

We move all terms to the left:

131/2x-21x-(23)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We add all the numbers together, and all the variables

-21x+131/2x-23=0

We multiply all the terms by the denominator


-21x*2x-23*2x+131=0

Wy multiply elements

-42x^2-46x+131=0

a = -42; b = -46; c = +131;
Δ = b2-4ac
Δ = -462-4·(-42)·131
Δ = 24124
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{24124}=\sqrt{4*6031}=\sqrt{4}*\sqrt{6031}=2\sqrt{6031}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-46)-2\sqrt{6031}}{2*-42}=\frac{46-2\sqrt{6031}}{-84}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-46)+2\sqrt{6031}}{2*-42}=\frac{46+2\sqrt{6031}}{-84}
$