x+(x+100)+1/2x=1850

Solution for x+(x+100)+1/2x=1850 equation:

x+(x+100)+1/2x=1850

We move all terms to the left:

x+(x+100)+1/2x-(1850)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We get rid of parentheses

x+x+1/2x+100-1850=0

We multiply all the terms by the denominator


x*2x+x*2x+100*2x-1850*2x+1=0

Wy multiply elements

2x^2+2x^2+200x-3700x+1=0

We add all the numbers together, and all the variables

4x^2-3500x+1=0

a = 4; b = -3500; c = +1;
Δ = b2-4ac
Δ = -35002-4·4·1
Δ = 12249984
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:

$\sqrt{\Delta}=\sqrt{12249984}=\sqrt{64*191406}=\sqrt{64}*\sqrt{191406}=8\sqrt{191406}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3500)-8\sqrt{191406}}{2*4}=\frac{3500-8\sqrt{191406}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3500)+8\sqrt{191406}}{2*4}=\frac{3500+8\sqrt{191406}}{8}
$