X+6/4x=24

Solution for X+6/4x=24 equation:

X+6/4X=24

We move all terms to the left:

X+6/4X-(24)=0


Domain of the equation: 4X!=0

X!=0/4

X!=0

X∈R


We multiply all the terms by the denominator


X*4X-24*4X+6=0

Wy multiply elements

4X^2-96X+6=0

a = 4; b = -96; c = +6;
Δ = b2-4ac
Δ = -962-4·4·6
Δ = 9120
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:

$\sqrt{\Delta}=\sqrt{9120}=\sqrt{16*570}=\sqrt{16}*\sqrt{570}=4\sqrt{570}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-96)-4\sqrt{570}}{2*4}=\frac{96-4\sqrt{570}}{8}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-96)+4\sqrt{570}}{2*4}=\frac{96+4\sqrt{570}}{8}
$