(8/6)x=3/4

Solution for (8/6)x=3/4 equation:

(8/6)x=3/4

We move all terms to the left:

(8/6)x-(3/4)=0


Domain of the equation: 6)x!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

(+8/6)x-(+3/4)=0

We multiply parentheses

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

We get rid of parentheses

8x^2-3/4=0

We multiply all the terms by the denominator


8x^2*4-3=0

Wy multiply elements

32x^2-3=0

a = 32; b = 0; c = -3;
Δ = b2-4ac
Δ = 02-4·32·(-3)
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*32}=\frac{0-8\sqrt{6}}{64}
=-\frac{8\sqrt{6}}{64}
=-\frac{\sqrt{6}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+8\sqrt{6}}{2*32}=\frac{0+8\sqrt{6}}{64}
=\frac{8\sqrt{6}}{64}
=\frac{\sqrt{6}}{8}
$