-5/2x-3=-7/4x

Solution for -5/2x-3=-7/4x equation:

-5/2x-3=-7/4x

We move all terms to the left:

-5/2x-3-(-7/4x)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R



Domain of the equation: 4x)!=0

x!=0/1

x!=0

x∈R


We get rid of parentheses

-5/2x+7/4x-3=0

We calculate fractions


(-20x)/8x^2+14x/8x^2-3=0

We multiply all the terms by the denominator


(-20x)+14x-3*8x^2=0

We add all the numbers together, and all the variables

14x+(-20x)-3*8x^2=0

Wy multiply elements

-24x^2+14x+(-20x)=0

We get rid of parentheses

-24x^2+14x-20x=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{0}{-48}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+6}{2*-24}=\frac{12}{-48}
=-1/4
$