8x-4/6x=-3+8

Solution for 8x-4/6x=-3+8 equation:

8x-4/6x=-3+8

We move all terms to the left:

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


Domain of the equation: 6x!=0

x!=0/6

x!=0

x∈R


We add all the numbers together, and all the variables

8x-4/6x-5=0

We multiply all the terms by the denominator


8x*6x-5*6x-4=0

Wy multiply elements

48x^2-30x-4=0

a = 48; b = -30; c = -4;
Δ = b2-4ac
Δ = -302-4·48·(-4)
Δ = 1668
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:

$\sqrt{\Delta}=\sqrt{1668}=\sqrt{4*417}=\sqrt{4}*\sqrt{417}=2\sqrt{417}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-30)-2\sqrt{417}}{2*48}=\frac{30-2\sqrt{417}}{96}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-30)+2\sqrt{417}}{2*48}=\frac{30+2\sqrt{417}}{96}
$