5x-7/3x+27=180

Solution for 5x-7/3x+27=180 equation:

5x-7/3x+27=180

We move all terms to the left:

5x-7/3x+27-(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

5x-7/3x-153=0

We multiply all the terms by the denominator


5x*3x-153*3x-7=0

Wy multiply elements

15x^2-459x-7=0

a = 15; b = -459; c = -7;
Δ = b2-4ac
Δ = -4592-4·15·(-7)
Δ = 211101
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-459)-\sqrt{211101}}{2*15}=\frac{459-\sqrt{211101}}{30}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-459)+\sqrt{211101}}{2*15}=\frac{459+\sqrt{211101}}{30}
$