(x-10)+(2x-123)+(1/2x+5)=180

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Solution for (x-10)+(2x-123)+(1/2x+5)=180 equation:



(x-10)+(2x-123)+(1/2x+5)=180
We move all terms to the left:
(x-10)+(2x-123)+(1/2x+5)-(180)=0
Domain of the equation: 2x+5)!=0
x∈R
We get rid of parentheses
x+2x+1/2x-10-123+5-180=0
We multiply all the terms by the denominator
x*2x+2x*2x-10*2x-123*2x+5*2x-180*2x+1=0
Wy multiply elements
2x^2+4x^2-20x-246x+10x-360x+1=0
We add all the numbers together, and all the variables
6x^2-616x+1=0
a = 6; b = -616; c = +1;
Δ = b2-4ac
Δ = -6162-4·6·1
Δ = 379432
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:
$\sqrt{\Delta}=\sqrt{379432}=\sqrt{4*94858}=\sqrt{4}*\sqrt{94858}=2\sqrt{94858}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-616)-2\sqrt{94858}}{2*6}=\frac{616-2\sqrt{94858}}{12} $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-616)+2\sqrt{94858}}{2*6}=\frac{616+2\sqrt{94858}}{12} $

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