1/2x=18+5X

Solution for 1/2x=18+5X equation:

1/2x=18+5x

We move all terms to the left:

1/2x-(18+5x)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We add all the numbers together, and all the variables

1/2x-(5x+18)=0

We get rid of parentheses

1/2x-5x-18=0

We multiply all the terms by the denominator


-5x*2x-18*2x+1=0

Wy multiply elements

-10x^2-36x+1=0

a = -10; b = -36; c = +1;
Δ = b2-4ac
Δ = -362-4·(-10)·1
Δ = 1336
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:

$\sqrt{\Delta}=\sqrt{1336}=\sqrt{4*334}=\sqrt{4}*\sqrt{334}=2\sqrt{334}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-36)-2\sqrt{334}}{2*-10}=\frac{36-2\sqrt{334}}{-20}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-36)+2\sqrt{334}}{2*-10}=\frac{36+2\sqrt{334}}{-20}
$