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

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

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

We move all terms to the left:

2/5x+3/5x+x+30+x-(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+2/5x+3/5x-330=0

We multiply all the terms by the denominator


2x*5x-330*5x+2+3=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}
$