3x+3/5x=18

Solution for 3x+3/5x=18 equation:

3x+3/5x=18

We move all terms to the left:

3x+3/5x-(18)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R


We multiply all the terms by the denominator


3x*5x-18*5x+3=0

Wy multiply elements

15x^2-90x+3=0

a = 15; b = -90; c = +3;
Δ = b2-4ac
Δ = -902-4·15·3
Δ = 7920
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:

$\sqrt{\Delta}=\sqrt{7920}=\sqrt{144*55}=\sqrt{144}*\sqrt{55}=12\sqrt{55}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-90)-12\sqrt{55}}{2*15}=\frac{90-12\sqrt{55}}{30}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-90)+12\sqrt{55}}{2*15}=\frac{90+12\sqrt{55}}{30}
$