(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+15)!=0

x∈R


We get rid of parentheses

1/2x+2x+15-50-180=0

We multiply all the terms by the denominator


2x*2x+15*2x-50*2x-180*2x+1=0

Wy multiply elements

4x^2+30x-100x-360x+1=0

We add all the numbers together, and all the variables

4x^2-430x+1=0

a = 4; b = -430; c = +1;
Δ = b2-4ac
Δ = -4302-4·4·1
Δ = 184884
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:

$\sqrt{\Delta}=\sqrt{184884}=\sqrt{4*46221}=\sqrt{4}*\sqrt{46221}=2\sqrt{46221}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-430)-2\sqrt{46221}}{2*4}=\frac{430-2\sqrt{46221}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-430)+2\sqrt{46221}}{2*4}=\frac{430+2\sqrt{46221}}{8}
$