(1/2x+16)+(4x-293)+(x-27)=180

Solution for (1/2x+16)+(4x-293)+(x-27)=180 equation:

(1/2x+16)+(4x-293)+(x-27)=180

We move all terms to the left:

(1/2x+16)+(4x-293)+(x-27)-(180)=0


Domain of the equation: 2x+16)!=0

x∈R


We get rid of parentheses

1/2x+4x+x+16-293-27-180=0

We multiply all the terms by the denominator


4x*2x+x*2x+16*2x-293*2x-27*2x-180*2x+1=0

Wy multiply elements

8x^2+2x^2+32x-586x-54x-360x+1=0

We add all the numbers together, and all the variables

10x^2-968x+1=0

a = 10; b = -968; c = +1;
Δ = b2-4ac
Δ = -9682-4·10·1
Δ = 936984
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:

$\sqrt{\Delta}=\sqrt{936984}=\sqrt{4*234246}=\sqrt{4}*\sqrt{234246}=2\sqrt{234246}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-968)-2\sqrt{234246}}{2*10}=\frac{968-2\sqrt{234246}}{20}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-968)+2\sqrt{234246}}{2*10}=\frac{968+2\sqrt{234246}}{20}
$