0.5+x=3/4x

Solution for 0.5+x=3/4x equation:

0.5+x=3/4x

We move all terms to the left:

0.5+x-(3/4x)=0


Domain of the equation: 4x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

x-(+3/4x)+0.5=0

We get rid of parentheses

x-3/4x+0.5=0

We multiply all the terms by the denominator


x*4x+(0.5)*4x-3=0

We multiply parentheses

x*4x+2x-3=0

Wy multiply elements

4x^2+2x-3=0

a = 4; b = 2; c = -3;
Δ = b2-4ac
Δ = 22-4·4·(-3)
Δ = 52
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:

$\sqrt{\Delta}=\sqrt{52}=\sqrt{4*13}=\sqrt{4}*\sqrt{13}=2\sqrt{13}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-2\sqrt{13}}{2*4}=\frac{-2-2\sqrt{13}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2\sqrt{13}}{2*4}=\frac{-2+2\sqrt{13}}{8}
$