22x+1+9x-3/3x=180

Solution for 22x+1+9x-3/3x=180 equation:

22x+1+9x-3/3x=180

We move all terms to the left:

22x+1+9x-3/3x-(180)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We add all the numbers together, and all the variables

31x-3/3x-179=0

We multiply all the terms by the denominator


31x*3x-179*3x-3=0

Wy multiply elements

93x^2-537x-3=0

a = 93; b = -537; c = -3;
Δ = b2-4ac
Δ = -5372-4·93·(-3)
Δ = 289485
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:

$\sqrt{\Delta}=\sqrt{289485}=\sqrt{9*32165}=\sqrt{9}*\sqrt{32165}=3\sqrt{32165}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-537)-3\sqrt{32165}}{2*93}=\frac{537-3\sqrt{32165}}{186}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-537)+3\sqrt{32165}}{2*93}=\frac{537+3\sqrt{32165}}{186}
$