190=X+1/2x

Solution for 190=X+1/2x equation:

190=X+1/2X

We move all terms to the left:

190-(X+1/2X)=0


Domain of the equation: 2X)!=0

X!=0/1

X!=0

X∈R


We add all the numbers together, and all the variables

-(+X+1/2X)+190=0

We get rid of parentheses

-X-1/2X+190=0

We multiply all the terms by the denominator


-X*2X+190*2X-1=0

Wy multiply elements

-2X^2+380X-1=0

a = -2; b = 380; c = -1;
Δ = b2-4ac
Δ = 3802-4·(-2)·(-1)
Δ = 144392
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:

$\sqrt{\Delta}=\sqrt{144392}=\sqrt{4*36098}=\sqrt{4}*\sqrt{36098}=2\sqrt{36098}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(380)-2\sqrt{36098}}{2*-2}=\frac{-380-2\sqrt{36098}}{-4}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(380)+2\sqrt{36098}}{2*-2}=\frac{-380+2\sqrt{36098}}{-4}
$