(x-30)+(2x-120)+(1/2x-15)=180

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Solution for (x-30)+(2x-120)+(1/2x-15)=180 equation:



(x-30)+(2x-120)+(1/2x-15)=180
We move all terms to the left:
(x-30)+(2x-120)+(1/2x-15)-(180)=0
Domain of the equation: 2x-15)!=0
x∈R
We get rid of parentheses
x+2x+1/2x-30-120-15-180=0
We multiply all the terms by the denominator
x*2x+2x*2x-30*2x-120*2x-15*2x-180*2x+1=0
Wy multiply elements
2x^2+4x^2-60x-240x-30x-360x+1=0
We add all the numbers together, and all the variables
6x^2-690x+1=0
a = 6; b = -690; c = +1;
Δ = b2-4ac
Δ = -6902-4·6·1
Δ = 476076
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:
$\sqrt{\Delta}=\sqrt{476076}=\sqrt{4*119019}=\sqrt{4}*\sqrt{119019}=2\sqrt{119019}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-690)-2\sqrt{119019}}{2*6}=\frac{690-2\sqrt{119019}}{12} $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-690)+2\sqrt{119019}}{2*6}=\frac{690+2\sqrt{119019}}{12} $

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