(2x-12)+(x+24)+(1/4x+51)=180

Solution for (2x-12)+(x+24)+(1/4x+51)=180 equation:

(2x-12)+(x+24)+(1/4x+51)=180

We move all terms to the left:

(2x-12)+(x+24)+(1/4x+51)-(180)=0


Domain of the equation: 4x+51)!=0

x∈R


We get rid of parentheses

2x+x+1/4x-12+24+51-180=0

We multiply all the terms by the denominator


2x*4x+x*4x-12*4x+24*4x+51*4x-180*4x+1=0

Wy multiply elements

8x^2+4x^2-48x+96x+204x-720x+1=0

We add all the numbers together, and all the variables

12x^2-468x+1=0

a = 12; b = -468; c = +1;
Δ = b2-4ac
Δ = -4682-4·12·1
Δ = 218976
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:

$\sqrt{\Delta}=\sqrt{218976}=\sqrt{16*13686}=\sqrt{16}*\sqrt{13686}=4\sqrt{13686}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-468)-4\sqrt{13686}}{2*12}=\frac{468-4\sqrt{13686}}{24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-468)+4\sqrt{13686}}{2*12}=\frac{468+4\sqrt{13686}}{24}
$