1/4x+25x=70

Solution for 1/4x+25x=70 equation:

1/4x+25x=70

We move all terms to the left:

1/4x+25x-(70)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R


We add all the numbers together, and all the variables

25x+1/4x-70=0

We multiply all the terms by the denominator


25x*4x-70*4x+1=0

Wy multiply elements

100x^2-280x+1=0

a = 100; b = -280; c = +1;
Δ = b2-4ac
Δ = -2802-4·100·1
Δ = 78000
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:

$\sqrt{\Delta}=\sqrt{78000}=\sqrt{400*195}=\sqrt{400}*\sqrt{195}=20\sqrt{195}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-280)-20\sqrt{195}}{2*100}=\frac{280-20\sqrt{195}}{200}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-280)+20\sqrt{195}}{2*100}=\frac{280+20\sqrt{195}}{200}
$