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

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

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

We move all terms to the left:

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


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R



Domain of the equation: 8x+5)!=0

x∈R


We get rid of parentheses

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

We calculate fractions


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

We multiply all the terms by the denominator


24x+10x-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
$