5/4x=-5/2x-2

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

5/4x=-5/2x-2

We move all terms to the left:

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


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R



Domain of the equation: 2x-2)!=0

x∈R


We get rid of parentheses

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

We calculate fractions


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

We multiply all the terms by the denominator


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

We add all the numbers together, and all the variables

30x+2*8x^2=0

Wy multiply elements

16x^2+30x=0

a = 16; b = 30; c = 0;
Δ = b2-4ac
Δ = 302-4·16·0
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*16}=\frac{-60}{32}
=-1+7/8
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(30)+30}{2*16}=\frac{0}{32}
=0
$