6x-4/8x=12

Solution for 6x-4/8x=12 equation:

6x-4/8x=12

We move all terms to the left:

6x-4/8x-(12)=0


Domain of the equation: 8x!=0

x!=0/8

x!=0

x∈R


We multiply all the terms by the denominator


6x*8x-12*8x-4=0

Wy multiply elements

48x^2-96x-4=0

a = 48; b = -96; c = -4;
Δ = b2-4ac
Δ = -962-4·48·(-4)
Δ = 9984
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:

$\sqrt{\Delta}=\sqrt{9984}=\sqrt{256*39}=\sqrt{256}*\sqrt{39}=16\sqrt{39}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-96)-16\sqrt{39}}{2*48}=\frac{96-16\sqrt{39}}{96}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-96)+16\sqrt{39}}{2*48}=\frac{96+16\sqrt{39}}{96}
$