3x-17+1/22x-5=180

Solution for 3x-17+1/22x-5=180 equation:

3x-17+1/22x-5=180

We move all terms to the left:

3x-17+1/22x-5-(180)=0


Domain of the equation: 22x!=0

x!=0/22

x!=0

x∈R


We add all the numbers together, and all the variables

3x+1/22x-202=0

We multiply all the terms by the denominator


3x*22x-202*22x+1=0

Wy multiply elements

66x^2-4444x+1=0

a = 66; b = -4444; c = +1;
Δ = b2-4ac
Δ = -44442-4·66·1
Δ = 19748872
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:

$\sqrt{\Delta}=\sqrt{19748872}=\sqrt{4*4937218}=\sqrt{4}*\sqrt{4937218}=2\sqrt{4937218}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4444)-2\sqrt{4937218}}{2*66}=\frac{4444-2\sqrt{4937218}}{132}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4444)+2\sqrt{4937218}}{2*66}=\frac{4444+2\sqrt{4937218}}{132}
$