(3x+60)+(1/4x+55)=180

Solution for (3x+60)+(1/4x+55)=180 equation:

(3x+60)+(1/4x+55)=180

We move all terms to the left:

(3x+60)+(1/4x+55)-(180)=0


Domain of the equation: 4x+55)!=0

x∈R


We get rid of parentheses

3x+1/4x+60+55-180=0

We multiply all the terms by the denominator


3x*4x+60*4x+55*4x-180*4x+1=0

Wy multiply elements

12x^2+240x+220x-720x+1=0

We add all the numbers together, and all the variables

12x^2-260x+1=0

a = 12; b = -260; c = +1;
Δ = b2-4ac
Δ = -2602-4·12·1
Δ = 67552
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:

$\sqrt{\Delta}=\sqrt{67552}=\sqrt{16*4222}=\sqrt{16}*\sqrt{4222}=4\sqrt{4222}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-260)-4\sqrt{4222}}{2*12}=\frac{260-4\sqrt{4222}}{24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-260)+4\sqrt{4222}}{2*12}=\frac{260+4\sqrt{4222}}{24}
$