3/4x+3=-1+5/8x

Solution for 3/4x+3=-1+5/8x equation:

3/4x+3=-1+5/8x

We move all terms to the left:

3/4x+3-(-1+5/8x)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R



Domain of the equation: 8x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

3/4x-(5/8x-1)+3=0

We get rid of parentheses

3/4x-5/8x+1+3=0

We calculate fractions


24x/32x^2+(-20x)/32x^2+1+3=0

We add all the numbers together, and all the variables

24x/32x^2+(-20x)/32x^2+4=0

We multiply all the terms by the denominator


24x+(-20x)+4*32x^2=0

Wy multiply elements

128x^2+24x+(-20x)=0

We get rid of parentheses

128x^2+24x-20x=0

We add all the numbers together, and all the variables

128x^2+4x=0

a = 128; b = 4; c = 0;
Δ = b2-4ac
Δ = 42-4·128·0
Δ = 16
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{16}=4$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-4}{2*128}=\frac{-8}{256}
=-1/32
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+4}{2*128}=\frac{0}{256}
=0
$