5x+2/3x=180

Solution for 5x+2/3x=180 equation:

5x+2/3x=180

We move all terms to the left:

5x+2/3x-(180)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We multiply all the terms by the denominator


5x*3x-180*3x+2=0

Wy multiply elements

15x^2-540x+2=0

a = 15; b = -540; c = +2;
Δ = b2-4ac
Δ = -5402-4·15·2
Δ = 291480
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:

$\sqrt{\Delta}=\sqrt{291480}=\sqrt{4*72870}=\sqrt{4}*\sqrt{72870}=2\sqrt{72870}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-540)-2\sqrt{72870}}{2*15}=\frac{540-2\sqrt{72870}}{30}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-540)+2\sqrt{72870}}{2*15}=\frac{540+2\sqrt{72870}}{30}
$