x+x+3/5x=117

Solution for x+x+3/5x=117 equation:

x+x+3/5x=117

We move all terms to the left:

x+x+3/5x-(117)=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-117=0

We multiply all the terms by the denominator


2x*5x-117*5x+3=0

Wy multiply elements

10x^2-585x+3=0

a = 10; b = -585; c = +3;
Δ = b2-4ac
Δ = -5852-4·10·3
Δ = 342105
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{-(-585)-\sqrt{342105}}{2*10}=\frac{585-\sqrt{342105}}{20}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-585)+\sqrt{342105}}{2*10}=\frac{585+\sqrt{342105}}{20}
$