10x-1/24x+20)=30

Solution for 10x-1/24x+20)=30 equation:

10x-1/24x+20)=30

We move all terms to the left:

10x-1/24x+20)-(30)=0


Domain of the equation: 24x!=0

x!=0/24

x!=0

x∈R


We add all the numbers together, and all the variables

10x-1/24x=0

We multiply all the terms by the denominator


10x*24x-1=0

Wy multiply elements

240x^2-1=0

a = 240; b = 0; c = -1;
Δ = b2-4ac
Δ = 02-4·240·(-1)
Δ = 960
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:

$\sqrt{\Delta}=\sqrt{960}=\sqrt{64*15}=\sqrt{64}*\sqrt{15}=8\sqrt{15}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-8\sqrt{15}}{2*240}=\frac{0-8\sqrt{15}}{480}
=-\frac{8\sqrt{15}}{480}
=-\frac{\sqrt{15}}{60}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+8\sqrt{15}}{2*240}=\frac{0+8\sqrt{15}}{480}
=\frac{8\sqrt{15}}{480}
=\frac{\sqrt{15}}{60}
$