X+5/3x=180

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

X+5/3X=180

We move all terms to the left:

X+5/3X-(180)=0


Domain of the equation: 3X!=0

X!=0/3

X!=0

X∈R


We multiply all the terms by the denominator


X*3X-180*3X+5=0

Wy multiply elements

3X^2-540X+5=0

a = 3; b = -540; c = +5;
Δ = b2-4ac
Δ = -5402-4·3·5
Δ = 291540
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:

$\sqrt{\Delta}=\sqrt{291540}=\sqrt{4*72885}=\sqrt{4}*\sqrt{72885}=2\sqrt{72885}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-540)-2\sqrt{72885}}{2*3}=\frac{540-2\sqrt{72885}}{6}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-540)+2\sqrt{72885}}{2*3}=\frac{540+2\sqrt{72885}}{6}
$