x/7x-3x-8=24

Solution for x/7x-3x-8=24 equation:

x/7x-3x-8=24

We move all terms to the left:

x/7x-3x-8-(24)=0


Domain of the equation: 7x!=0

x!=0/7

x!=0

x∈R


We add all the numbers together, and all the variables

-3x+x/7x-32=0

We multiply all the terms by the denominator


-3x*7x+x-32*7x=0

We add all the numbers together, and all the variables

x-3x*7x-32*7x=0

Wy multiply elements

-21x^2+x-224x=0

We add all the numbers together, and all the variables

-21x^2-223x=0

a = -21; b = -223; c = 0;
Δ = b2-4ac
Δ = -2232-4·(-21)·0
Δ = 49729
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{49729}=223$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-223)-223}{2*-21}=\frac{0}{-42}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-223)+223}{2*-21}=\frac{446}{-42}
=-10+13/21
$