1/24x-8+3x=36

Solution for 1/24x-8+3x=36 equation:

1/24x-8+3x=36

We move all terms to the left:

1/24x-8+3x-(36)=0


Domain of the equation: 24x!=0

x!=0/24

x!=0

x∈R


We add all the numbers together, and all the variables

3x+1/24x-44=0

We multiply all the terms by the denominator


3x*24x-44*24x+1=0

Wy multiply elements

72x^2-1056x+1=0

a = 72; b = -1056; c = +1;
Δ = b2-4ac
Δ = -10562-4·72·1
Δ = 1114848
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:

$\sqrt{\Delta}=\sqrt{1114848}=\sqrt{7056*158}=\sqrt{7056}*\sqrt{158}=84\sqrt{158}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1056)-84\sqrt{158}}{2*72}=\frac{1056-84\sqrt{158}}{144}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1056)+84\sqrt{158}}{2*72}=\frac{1056+84\sqrt{158}}{144}
$