x+30+x+2/5x+35x=360

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Solution for x+30+x+2/5x+35x=360 equation: 



x+30+x+2/5x+35x=360

We move all terms to the left:

x+30+x+2/5x+35x-(360)=0



Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R



We add all the numbers together, and all the variables

37x+2/5x-330=0

We multiply all the terms by the denominator


37x*5x-330*5x+2=0

Wy multiply elements

185x^2-1650x+2=0

a = 185; b = -1650; c = +2;
Δ = b2-4ac
Δ = -16502-4·185·2
Δ = 2721020
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:


$\sqrt{\Delta}=\sqrt{2721020}=\sqrt{4*680255}=\sqrt{4}*\sqrt{680255}=2\sqrt{680255}$


$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1650)-2\sqrt{680255}}{2*185}=\frac{1650-2\sqrt{680255}}{370}
$


$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1650)+2\sqrt{680255}}{2*185}=\frac{1650+2\sqrt{680255}}{370}
$

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