(x-24)+(2x-53)+(1/2x+12)=180

Solution for (x-24)+(2x-53)+(1/2x+12)=180 equation:

(x-24)+(2x-53)+(1/2x+12)=180

We move all terms to the left:

(x-24)+(2x-53)+(1/2x+12)-(180)=0


Domain of the equation: 2x+12)!=0

x∈R


We get rid of parentheses

x+2x+1/2x-24-53+12-180=0

We multiply all the terms by the denominator


x*2x+2x*2x-24*2x-53*2x+12*2x-180*2x+1=0

Wy multiply elements

2x^2+4x^2-48x-106x+24x-360x+1=0

We add all the numbers together, and all the variables

6x^2-490x+1=0

a = 6; b = -490; c = +1;
Δ = b2-4ac
Δ = -4902-4·6·1
Δ = 240076
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:

$\sqrt{\Delta}=\sqrt{240076}=\sqrt{4*60019}=\sqrt{4}*\sqrt{60019}=2\sqrt{60019}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-490)-2\sqrt{60019}}{2*6}=\frac{490-2\sqrt{60019}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-490)+2\sqrt{60019}}{2*6}=\frac{490+2\sqrt{60019}}{12}
$