8x=10/12x=6

Solution for 8x=10/12x=6 equation:

8x=10/12x=6

We move all terms to the left:

8x-(10/12x)=0


Domain of the equation: 12x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

8x-(+10/12x)=0

We get rid of parentheses

8x-10/12x=0

We multiply all the terms by the denominator


8x*12x-10=0

Wy multiply elements

96x^2-10=0

a = 96; b = 0; c = -10;
Δ = b2-4ac
Δ = 02-4·96·(-10)
Δ = 3840
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:

$\sqrt{\Delta}=\sqrt{3840}=\sqrt{256*15}=\sqrt{256}*\sqrt{15}=16\sqrt{15}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-16\sqrt{15}}{2*96}=\frac{0-16\sqrt{15}}{192}
=-\frac{16\sqrt{15}}{192}
=-\frac{\sqrt{15}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+16\sqrt{15}}{2*96}=\frac{0+16\sqrt{15}}{192}
=\frac{16\sqrt{15}}{192}
=\frac{\sqrt{15}}{12}
$