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

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

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

We move all terms to the left:

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


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R



Domain of the equation: 2x+3)!=0

x∈R


We get rid of parentheses

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

We calculate fractions


10x/8x^2+20x/8x^2-3=0

We multiply all the terms by the denominator


10x+20x-3*8x^2=0

We add all the numbers together, and all the variables

30x-3*8x^2=0

Wy multiply elements

-24x^2+30x=0

a = -24; b = 30; c = 0;
Δ = b2-4ac
Δ = 302-4·(-24)·0
Δ = 900
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{900}=30$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(30)-30}{2*-24}=\frac{-60}{-48}
=1+1/4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(30)+30}{2*-24}=\frac{0}{-48}
=0
$