1/2x+15-2x-50=180

Solution for 1/2x+15-2x-50=180 equation:

1/2x+15-2x-50=180

We move all terms to the left:

1/2x+15-2x-50-(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-215=0

We multiply all the terms by the denominator


-2x*2x-215*2x+1=0

Wy multiply elements

-4x^2-430x+1=0

a = -4; b = -430; c = +1;
Δ = b2-4ac
Δ = -4302-4·(-4)·1
Δ = 184916
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:

$\sqrt{\Delta}=\sqrt{184916}=\sqrt{4*46229}=\sqrt{4}*\sqrt{46229}=2\sqrt{46229}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-430)-2\sqrt{46229}}{2*-4}=\frac{430-2\sqrt{46229}}{-8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-430)+2\sqrt{46229}}{2*-4}=\frac{430+2\sqrt{46229}}{-8}
$