5/8x+5=-3/2x

Solution for 5/8x+5=-3/2x equation:

5/8x+5=-3/2x

We move all terms to the left:

5/8x+5-(-3/2x)=0


Domain of the equation: 8x!=0

x!=0/8

x!=0

x∈R



Domain of the equation: 2x)!=0

x!=0/1

x!=0

x∈R


We get rid of parentheses

5/8x+3/2x+5=0

We calculate fractions


10x/16x^2+24x/16x^2+5=0

We multiply all the terms by the denominator


10x+24x+5*16x^2=0

We add all the numbers together, and all the variables

34x+5*16x^2=0

Wy multiply elements

80x^2+34x=0

a = 80; b = 34; c = 0;
Δ = b2-4ac
Δ = 342-4·80·0
Δ = 1156
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1156}=34$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(34)-34}{2*80}=\frac{-68}{160}
=-17/40
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(34)+34}{2*80}=\frac{0}{160}
=0
$