x+30+x+3/5x+2/5x=360

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Solution for x+30+x+3/5x+2/5x=360 equation:



x+30+x+3/5x+2/5x=360
We move all terms to the left:
x+30+x+3/5x+2/5x-(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
2x+3/5x+2/5x-330=0
We multiply all the terms by the denominator
2x*5x-330*5x+3+2=0
We add all the numbers together, and all the variables
2x*5x-330*5x+5=0
Wy multiply elements
10x^2-1650x+5=0
a = 10; b = -1650; c = +5;
Δ = b2-4ac
Δ = -16502-4·10·5
Δ = 2722300
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:
$\sqrt{\Delta}=\sqrt{2722300}=\sqrt{100*27223}=\sqrt{100}*\sqrt{27223}=10\sqrt{27223}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1650)-10\sqrt{27223}}{2*10}=\frac{1650-10\sqrt{27223}}{20} $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1650)+10\sqrt{27223}}{2*10}=\frac{1650+10\sqrt{27223}}{20} $

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