2x+12+3/4x+27=180

Solution for 2x+12+3/4x+27=180 equation:

2x+12+3/4x+27=180

We move all terms to the left:

2x+12+3/4x+27-(180)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R


We add all the numbers together, and all the variables

2x+3/4x-141=0

We multiply all the terms by the denominator


2x*4x-141*4x+3=0

Wy multiply elements

8x^2-564x+3=0

a = 8; b = -564; c = +3;
Δ = b2-4ac
Δ = -5642-4·8·3
Δ = 318000
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:

$\sqrt{\Delta}=\sqrt{318000}=\sqrt{400*795}=\sqrt{400}*\sqrt{795}=20\sqrt{795}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-564)-20\sqrt{795}}{2*8}=\frac{564-20\sqrt{795}}{16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-564)+20\sqrt{795}}{2*8}=\frac{564+20\sqrt{795}}{16}
$