(5x-65)+(x+35)+(1/5x+55)=360

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Solution for (5x-65)+(x+35)+(1/5x+55)=360 equation: 



(5x-65)+(x+35)+(1/5x+55)=360

We move all terms to the left:

(5x-65)+(x+35)+(1/5x+55)-(360)=0



Domain of the equation: 5x+55)!=0

x∈R



We get rid of parentheses

5x+x+1/5x-65+35+55-360=0

We multiply all the terms by the denominator


5x*5x+x*5x-65*5x+35*5x+55*5x-360*5x+1=0

Wy multiply elements

25x^2+5x^2-325x+175x+275x-1800x+1=0

We add all the numbers together, and all the variables

30x^2-1675x+1=0

a = 30; b = -1675; c = +1;
Δ = b2-4ac
Δ = -16752-4·30·1
Δ = 2805505
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1675)-\sqrt{2805505}}{2*30}=\frac{1675-\sqrt{2805505}}{60}
$


$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1675)+\sqrt{2805505}}{2*30}=\frac{1675+\sqrt{2805505}}{60}
$

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