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

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

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

We move all terms to the left:

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


Domain of the equation: 2x+15)!=0

x∈R


We get rid of parentheses

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

We multiply all the terms by the denominator


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

Wy multiply elements

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

We add all the numbers together, and all the variables

8x^2-530x+1=0

a = 8; b = -530; c = +1;
Δ = b2-4ac
Δ = -5302-4·8·1
Δ = 280868
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:

$\sqrt{\Delta}=\sqrt{280868}=\sqrt{196*1433}=\sqrt{196}*\sqrt{1433}=14\sqrt{1433}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-530)-14\sqrt{1433}}{2*8}=\frac{530-14\sqrt{1433}}{16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-530)+14\sqrt{1433}}{2*8}=\frac{530+14\sqrt{1433}}{16}
$