8x-3/3x=21

Solution for 8x-3/3x=21 equation:

8x-3/3x=21

We move all terms to the left:

8x-3/3x-(21)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We multiply all the terms by the denominator


8x*3x-21*3x-3=0

Wy multiply elements

24x^2-63x-3=0

a = 24; b = -63; c = -3;
Δ = b2-4ac
Δ = -632-4·24·(-3)
Δ = 4257
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:

$\sqrt{\Delta}=\sqrt{4257}=\sqrt{9*473}=\sqrt{9}*\sqrt{473}=3\sqrt{473}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-63)-3\sqrt{473}}{2*24}=\frac{63-3\sqrt{473}}{48}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-63)+3\sqrt{473}}{2*24}=\frac{63+3\sqrt{473}}{48}
$