3x+171/2x-5=180

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Solution for 3x+171/2x-5=180 equation: 



3x+171/2x-5=180

We move all terms to the left:

3x+171/2x-5-(180)=0



Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R



We add all the numbers together, and all the variables

3x+171/2x-185=0

We multiply all the terms by the denominator


3x*2x-185*2x+171=0

Wy multiply elements

6x^2-370x+171=0

a = 6; b = -370; c = +171;
Δ = b2-4ac
Δ = -3702-4·6·171
Δ = 132796
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:


$\sqrt{\Delta}=\sqrt{132796}=\sqrt{4*33199}=\sqrt{4}*\sqrt{33199}=2\sqrt{33199}$


$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-370)-2\sqrt{33199}}{2*6}=\frac{370-2\sqrt{33199}}{12}
$


$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-370)+2\sqrt{33199}}{2*6}=\frac{370+2\sqrt{33199}}{12}
$

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