(1/2x+20)+(2x-10)=180

Solution for (1/2x+20)+(2x-10)=180 equation:

(1/2x+20)+(2x-10)=180

We move all terms to the left:

(1/2x+20)+(2x-10)-(180)=0


Domain of the equation: 2x+20)!=0

x∈R


We get rid of parentheses

1/2x+2x+20-10-180=0

We multiply all the terms by the denominator


2x*2x+20*2x-10*2x-180*2x+1=0

Wy multiply elements

4x^2+40x-20x-360x+1=0

We add all the numbers together, and all the variables

4x^2-340x+1=0

a = 4; b = -340; c = +1;
Δ = b2-4ac
Δ = -3402-4·4·1
Δ = 115584
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:

$\sqrt{\Delta}=\sqrt{115584}=\sqrt{64*1806}=\sqrt{64}*\sqrt{1806}=8\sqrt{1806}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-340)-8\sqrt{1806}}{2*4}=\frac{340-8\sqrt{1806}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-340)+8\sqrt{1806}}{2*4}=\frac{340+8\sqrt{1806}}{8}
$