7x-21/x+2*4x+8/x-3=0

Solution for 7x-21/x+2*4x+8/x-3=0 equation:

7x-21/x+2*4x+8/x-3=0


Domain of the equation: x!=0

x∈R


Wy multiply elements

7x-21/x+8x+8/x-3=0

We multiply all the terms by the denominator


7x*x+8x*x-3*x-21+8=0

We add all the numbers together, and all the variables

-3x+7x*x+8x*x-13=0

Wy multiply elements

7x^2+8x^2-3x-13=0

We add all the numbers together, and all the variables

15x^2-3x-13=0

a = 15; b = -3; c = -13;
Δ = b2-4ac
Δ = -32-4·15·(-13)
Δ = 789
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3)-\sqrt{789}}{2*15}=\frac{3-\sqrt{789}}{30}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+\sqrt{789}}{2*15}=\frac{3+\sqrt{789}}{30}
$