(4x+12)+(x+48)+(1/3x+56)=180

Solution for (4x+12)+(x+48)+(1/3x+56)=180 equation:

(4x+12)+(x+48)+(1/3x+56)=180

We move all terms to the left:

(4x+12)+(x+48)+(1/3x+56)-(180)=0


Domain of the equation: 3x+56)!=0

x∈R


We get rid of parentheses

4x+x+1/3x+12+48+56-180=0

We multiply all the terms by the denominator


4x*3x+x*3x+12*3x+48*3x+56*3x-180*3x+1=0

Wy multiply elements

12x^2+3x^2+36x+144x+168x-540x+1=0

We add all the numbers together, and all the variables

15x^2-192x+1=0

a = 15; b = -192; c = +1;
Δ = b2-4ac
Δ = -1922-4·15·1
Δ = 36804
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:

$\sqrt{\Delta}=\sqrt{36804}=\sqrt{4*9201}=\sqrt{4}*\sqrt{9201}=2\sqrt{9201}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-192)-2\sqrt{9201}}{2*15}=\frac{192-2\sqrt{9201}}{30}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-192)+2\sqrt{9201}}{2*15}=\frac{192+2\sqrt{9201}}{30}
$