1/4x+x=100

Solution for 1/4x+x=100 equation:

1/4x+x=100

We move all terms to the left:

1/4x+x-(100)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R


We add all the numbers together, and all the variables

x+1/4x-100=0

We multiply all the terms by the denominator


x*4x-100*4x+1=0

Wy multiply elements

4x^2-400x+1=0

a = 4; b = -400; c = +1;
Δ = b2-4ac
Δ = -4002-4·4·1
Δ = 159984
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:

$\sqrt{\Delta}=\sqrt{159984}=\sqrt{144*1111}=\sqrt{144}*\sqrt{1111}=12\sqrt{1111}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-400)-12\sqrt{1111}}{2*4}=\frac{400-12\sqrt{1111}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-400)+12\sqrt{1111}}{2*4}=\frac{400+12\sqrt{1111}}{8}
$