7+x=1/24x-2

Solution for 7+x=1/24x-2 equation:

7+x=1/24x-2

We move all terms to the left:

7+x-(1/24x-2)=0


Domain of the equation: 24x-2)!=0

x∈R


We get rid of parentheses

x-1/24x+2+7=0

We multiply all the terms by the denominator


x*24x+2*24x+7*24x-1=0

Wy multiply elements

24x^2+48x+168x-1=0

We add all the numbers together, and all the variables

24x^2+216x-1=0

a = 24; b = 216; c = -1;
Δ = b2-4ac
Δ = 2162-4·24·(-1)
Δ = 46752
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:

$\sqrt{\Delta}=\sqrt{46752}=\sqrt{16*2922}=\sqrt{16}*\sqrt{2922}=4\sqrt{2922}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(216)-4\sqrt{2922}}{2*24}=\frac{-216-4\sqrt{2922}}{48}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(216)+4\sqrt{2922}}{2*24}=\frac{-216+4\sqrt{2922}}{48}
$