3x+4=-1/24x

Solution for 3x+4=-1/24x equation:

3x+4=-1/24x

We move all terms to the left:

3x+4-(-1/24x)=0


Domain of the equation: 24x)!=0

x!=0/1

x!=0

x∈R


We get rid of parentheses

3x+1/24x+4=0

We multiply all the terms by the denominator


3x*24x+4*24x+1=0

Wy multiply elements

72x^2+96x+1=0

a = 72; b = 96; c = +1;
Δ = b2-4ac
Δ = 962-4·72·1
Δ = 8928
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:

$\sqrt{\Delta}=\sqrt{8928}=\sqrt{144*62}=\sqrt{144}*\sqrt{62}=12\sqrt{62}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(96)-12\sqrt{62}}{2*72}=\frac{-96-12\sqrt{62}}{144}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(96)+12\sqrt{62}}{2*72}=\frac{-96+12\sqrt{62}}{144}
$