6x+3/5x=18

Solution for 6x+3/5x=18 equation:

6x+3/5x=18

We move all terms to the left:

6x+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


6x*5x-18*5x+3=0

Wy multiply elements

30x^2-90x+3=0

a = 30; b = -90; c = +3;
Δ = b2-4ac
Δ = -902-4·30·3
Δ = 7740
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:

$\sqrt{\Delta}=\sqrt{7740}=\sqrt{36*215}=\sqrt{36}*\sqrt{215}=6\sqrt{215}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-90)-6\sqrt{215}}{2*30}=\frac{90-6\sqrt{215}}{60}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-90)+6\sqrt{215}}{2*30}=\frac{90+6\sqrt{215}}{60}
$