-5/8x+4=3/2x

Solution for -5/8x+4=3/2x equation:

-5/8x+4=3/2x

We move all terms to the left:

-5/8x+4-(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 add all the numbers together, and all the variables

-5/8x-(+3/2x)+4=0

We get rid of parentheses

-5/8x-3/2x+4=0

We calculate fractions


(-10x)/16x^2+(-24x)/16x^2+4=0

We multiply all the terms by the denominator


(-10x)+(-24x)+4*16x^2=0

Wy multiply elements

64x^2+(-10x)+(-24x)=0

We get rid of parentheses

64x^2-10x-24x=0

We add all the numbers together, and all the variables

64x^2-34x=0

a = 64; b = -34; c = 0;
Δ = b2-4ac
Δ = -342-4·64·0
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*64}=\frac{0}{128}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-34)+34}{2*64}=\frac{68}{128}
=17/32
$