2x+3+1/5x-5=180

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Solution for 2x+3+1/5x-5=180 equation: 



2x+3+1/5x-5=180

We move all terms to the left:

2x+3+1/5x-5-(180)=0



Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R



We add all the numbers together, and all the variables

2x+1/5x-182=0

We multiply all the terms by the denominator


2x*5x-182*5x+1=0

Wy multiply elements

10x^2-910x+1=0

a = 10; b = -910; c = +1;
Δ = b2-4ac
Δ = -9102-4·10·1
Δ = 828060
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:


$\sqrt{\Delta}=\sqrt{828060}=\sqrt{4*207015}=\sqrt{4}*\sqrt{207015}=2\sqrt{207015}$


$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-910)-2\sqrt{207015}}{2*10}=\frac{910-2\sqrt{207015}}{20}
$


$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-910)+2\sqrt{207015}}{2*10}=\frac{910+2\sqrt{207015}}{20}
$

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