-2x+5+1/2x-12=180

Solution for -2x+5+1/2x-12=180 equation:

-2x+5+1/2x-12=180

We move all terms to the left:

-2x+5+1/2x-12-(180)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We add all the numbers together, and all the variables

-2x+1/2x-187=0

We multiply all the terms by the denominator


-2x*2x-187*2x+1=0

Wy multiply elements

-4x^2-374x+1=0

a = -4; b = -374; c = +1;
Δ = b2-4ac
Δ = -3742-4·(-4)·1
Δ = 139892
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:

$\sqrt{\Delta}=\sqrt{139892}=\sqrt{4*34973}=\sqrt{4}*\sqrt{34973}=2\sqrt{34973}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-374)-2\sqrt{34973}}{2*-4}=\frac{374-2\sqrt{34973}}{-8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-374)+2\sqrt{34973}}{2*-4}=\frac{374+2\sqrt{34973}}{-8}
$