18-3/4x=5+1/2x

Solution for 18-3/4x=5+1/2x equation:

18-3/4x=5+1/2x

We move all terms to the left:

18-3/4x-(5+1/2x)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R



Domain of the equation: 2x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

-3/4x-(1/2x+5)+18=0

We get rid of parentheses

-3/4x-1/2x-5+18=0

We calculate fractions


(-6x)/8x^2+(-4x)/8x^2-5+18=0

We add all the numbers together, and all the variables

(-6x)/8x^2+(-4x)/8x^2+13=0

We multiply all the terms by the denominator


(-6x)+(-4x)+13*8x^2=0

Wy multiply elements

104x^2+(-6x)+(-4x)=0

We get rid of parentheses

104x^2-6x-4x=0

We add all the numbers together, and all the variables

104x^2-10x=0

a = 104; b = -10; c = 0;
Δ = b2-4ac
Δ = -102-4·104·0
Δ = 100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{100}=10$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-10}{2*104}=\frac{0}{208}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+10}{2*104}=\frac{20}{208}
=5/52
$