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

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

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

We move all terms to the left:

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


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R



Domain of the equation: 8x+4)!=0

x∈R


We get rid of parentheses

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

We calculate fractions


24x/32x^2+(-20x)/32x^2-4+3=0

We add all the numbers together, and all the variables

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

We multiply all the terms by the denominator


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

Wy multiply elements

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

We get rid of parentheses

-32x^2+24x-20x=0

We add all the numbers together, and all the variables

-32x^2+4x=0

a = -32; b = 4; c = 0;
Δ = b2-4ac
Δ = 42-4·(-32)·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*-32}=\frac{-8}{-64}
=1/8
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+4}{2*-32}=\frac{0}{-64}
=0
$