4x+8/6x-5=33

Solution for 4x+8/6x-5=33 equation:

4x+8/6x-5=33

We move all terms to the left:

4x+8/6x-5-(33)=0


Domain of the equation: 6x!=0

x!=0/6

x!=0

x∈R


We add all the numbers together, and all the variables

4x+8/6x-38=0

We multiply all the terms by the denominator


4x*6x-38*6x+8=0

Wy multiply elements

24x^2-228x+8=0

a = 24; b = -228; c = +8;
Δ = b2-4ac
Δ = -2282-4·24·8
Δ = 51216
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:

$\sqrt{\Delta}=\sqrt{51216}=\sqrt{16*3201}=\sqrt{16}*\sqrt{3201}=4\sqrt{3201}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-228)-4\sqrt{3201}}{2*24}=\frac{228-4\sqrt{3201}}{48}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-228)+4\sqrt{3201}}{2*24}=\frac{228+4\sqrt{3201}}{48}
$