2x+3+1/2x-4=172

Solution for 2x+3+1/2x-4=172 equation:

2x+3+1/2x-4=172

We move all terms to the left:

2x+3+1/2x-4-(172)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We add all the numbers together, and all the variables

2x+1/2x-173=0

We multiply all the terms by the denominator


2x*2x-173*2x+1=0

Wy multiply elements

4x^2-346x+1=0

a = 4; b = -346; c = +1;
Δ = b2-4ac
Δ = -3462-4·4·1
Δ = 119700
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:

$\sqrt{\Delta}=\sqrt{119700}=\sqrt{900*133}=\sqrt{900}*\sqrt{133}=30\sqrt{133}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-346)-30\sqrt{133}}{2*4}=\frac{346-30\sqrt{133}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-346)+30\sqrt{133}}{2*4}=\frac{346+30\sqrt{133}}{8}
$