(3/4)x+(5/8)=9/8

Solution for (3/4)x+(5/8)=9/8 equation:

(3/4)x+(5/8)=9/8

We move all terms to the left:

(3/4)x+(5/8)-(9/8)=0


Domain of the equation: 4)x!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

(+3/4)x+(+5/8)-(+9/8)=0

We multiply parentheses

3x^2+(+5/8)-(+9/8)=0

We get rid of parentheses

3x^2+5/8-9/8=0

We multiply all the terms by the denominator


3x^2*8+5-9=0

We add all the numbers together, and all the variables

3x^2*8-4=0

Wy multiply elements

24x^2-4=0

a = 24; b = 0; c = -4;
Δ = b2-4ac
Δ = 02-4·24·(-4)
Δ = 384
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{384}=\sqrt{64*6}=\sqrt{64}*\sqrt{6}=8\sqrt{6}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-8\sqrt{6}}{2*24}=\frac{0-8\sqrt{6}}{48}
=-\frac{8\sqrt{6}}{48}
=-\frac{\sqrt{6}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+8\sqrt{6}}{2*24}=\frac{0+8\sqrt{6}}{48}
=\frac{8\sqrt{6}}{48}
=\frac{\sqrt{6}}{6}
$