x+(2x-14)+(1/2x+12)=180

Solution for x+(2x-14)+(1/2x+12)=180 equation:

x+(2x-14)+(1/2x+12)=180

We move all terms to the left:

x+(2x-14)+(1/2x+12)-(180)=0


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

x∈R


We get rid of parentheses

x+2x+1/2x-14+12-180=0

We multiply all the terms by the denominator


x*2x+2x*2x-14*2x+12*2x-180*2x+1=0

Wy multiply elements

2x^2+4x^2-28x+24x-360x+1=0

We add all the numbers together, and all the variables

6x^2-364x+1=0

a = 6; b = -364; c = +1;
Δ = b2-4ac
Δ = -3642-4·6·1
Δ = 132472
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:

$\sqrt{\Delta}=\sqrt{132472}=\sqrt{4*33118}=\sqrt{4}*\sqrt{33118}=2\sqrt{33118}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-364)-2\sqrt{33118}}{2*6}=\frac{364-2\sqrt{33118}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-364)+2\sqrt{33118}}{2*6}=\frac{364+2\sqrt{33118}}{12}
$