8x/x+3-8=x-21/x-3

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

8x/x+3-8=x-21/x-3

We move all terms to the left:

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


Domain of the equation: x!=0

x∈R



Domain of the equation: x-3)!=0

x∈R


We add all the numbers together, and all the variables

8x/x-(x-21/x-3)-5=0

We get rid of parentheses

8x/x-x+21/x+3-5=0

We multiply all the terms by the denominator


8x-x*x+3*x-5*x+21=0

We add all the numbers together, and all the variables

6x-x*x+21=0

Wy multiply elements

-1x^2+6x+21=0

a = -1; b = 6; c = +21;
Δ = b2-4ac
Δ = 62-4·(-1)·21
Δ = 120
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:

$\sqrt{\Delta}=\sqrt{120}=\sqrt{4*30}=\sqrt{4}*\sqrt{30}=2\sqrt{30}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-2\sqrt{30}}{2*-1}=\frac{-6-2\sqrt{30}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+2\sqrt{30}}{2*-1}=\frac{-6+2\sqrt{30}}{-2}
$