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

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

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

We move all terms to the left:

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


Domain of the equation: 2x+20+2x-10)!=0

We move all terms containing x to the left, all other terms to the right

2x+2x-10)!=-20

x∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We multiply all the terms by the denominator


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

Wy multiply elements

-4x^2-20x+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}
$