2x-10+1/2x+20=180

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Solution for 2x-10+1/2x+20=180 equation: 



2x-10+1/2x+20=180

We move all terms to the left:

2x-10+1/2x+20-(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

2x+1/2x-170=0

We multiply all the terms by the denominator


2x*2x-170*2x+1=0

Wy multiply elements

4x^2-340x+1=0

a = 4; b = -340; c = +1;
Δ = b2-4ac
Δ = -3402-4·4·1
Δ = 115584
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:


$\sqrt{\Delta}=\sqrt{115584}=\sqrt{64*1806}=\sqrt{64}*\sqrt{1806}=8\sqrt{1806}$


$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-340)-8\sqrt{1806}}{2*4}=\frac{340-8\sqrt{1806}}{8}
$


$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-340)+8\sqrt{1806}}{2*4}=\frac{340+8\sqrt{1806}}{8}
$

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