2x+3/3x+7=180

Solution for 2x+3/3x+7=180 equation:

2x+3/3x+7=180

We move all terms to the left:

2x+3/3x+7-(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

2x+3/3x-173=0

We multiply all the terms by the denominator


2x*3x-173*3x+3=0

Wy multiply elements

6x^2-519x+3=0

a = 6; b = -519; c = +3;
Δ = b2-4ac
Δ = -5192-4·6·3
Δ = 269289
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:

$\sqrt{\Delta}=\sqrt{269289}=\sqrt{9*29921}=\sqrt{9}*\sqrt{29921}=3\sqrt{29921}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-519)-3\sqrt{29921}}{2*6}=\frac{519-3\sqrt{29921}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-519)+3\sqrt{29921}}{2*6}=\frac{519+3\sqrt{29921}}{12}
$