6x+1/4x=25

Solution for 6x+1/4x=25 equation:

6x+1/4x=25

We move all terms to the left:

6x+1/4x-(25)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R


We multiply all the terms by the denominator


6x*4x-25*4x+1=0

Wy multiply elements

24x^2-100x+1=0

a = 24; b = -100; c = +1;
Δ = b2-4ac
Δ = -1002-4·24·1
Δ = 9904
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:

$\sqrt{\Delta}=\sqrt{9904}=\sqrt{16*619}=\sqrt{16}*\sqrt{619}=4\sqrt{619}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-100)-4\sqrt{619}}{2*24}=\frac{100-4\sqrt{619}}{48}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-100)+4\sqrt{619}}{2*24}=\frac{100+4\sqrt{619}}{48}
$