2x-5+3=18/2x=20

Solution for 2x-5+3=18/2x=20 equation:

2x-5+3=18/2x=20

We move all terms to the left:

2x-5+3-(18/2x)=0


Domain of the equation: 2x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

2x-(+18/2x)-5+3=0

We add all the numbers together, and all the variables

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

We get rid of parentheses

2x-18/2x-2=0

We multiply all the terms by the denominator


2x*2x-2*2x-18=0

Wy multiply elements

4x^2-4x-18=0

a = 4; b = -4; c = -18;
Δ = b2-4ac
Δ = -42-4·4·(-18)
Δ = 304
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:

$\sqrt{\Delta}=\sqrt{304}=\sqrt{16*19}=\sqrt{16}*\sqrt{19}=4\sqrt{19}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-4\sqrt{19}}{2*4}=\frac{4-4\sqrt{19}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+4\sqrt{19}}{2*4}=\frac{4+4\sqrt{19}}{8}
$