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

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

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

We move all terms to the left:

5/4x-(-3+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

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

We get rid of parentheses

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

We calculate fractions


10x/8x^2+(-4x)/8x^2+3=0

We multiply all the terms by the denominator


10x+(-4x)+3*8x^2=0

Wy multiply elements

24x^2+10x+(-4x)=0

We get rid of parentheses

24x^2+10x-4x=0

We add all the numbers together, and all the variables

24x^2+6x=0

a = 24; b = 6; c = 0;
Δ = b2-4ac
Δ = 62-4·24·0
Δ = 36
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{36}=6$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-6}{2*24}=\frac{-12}{48}
=-1/4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+6}{2*24}=\frac{0}{48}
=0
$