10x+1/4x=164

Solution for 10x+1/4x=164 equation:

10x+1/4x=164

We move all terms to the left:

10x+1/4x-(164)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R


We multiply all the terms by the denominator


10x*4x-164*4x+1=0

Wy multiply elements

40x^2-656x+1=0

a = 40; b = -656; c = +1;
Δ = b2-4ac
Δ = -6562-4·40·1
Δ = 430176
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:

$\sqrt{\Delta}=\sqrt{430176}=\sqrt{16*26886}=\sqrt{16}*\sqrt{26886}=4\sqrt{26886}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-656)-4\sqrt{26886}}{2*40}=\frac{656-4\sqrt{26886}}{80}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-656)+4\sqrt{26886}}{2*40}=\frac{656+4\sqrt{26886}}{80}
$