x2+x+x/4=104

Solution for x2+x+x/4=104 equation:

x2+x+x/4=104

We move all terms to the left:

x2+x+x/4-(104)=0

We add all the numbers together, and all the variables

x^2+x+x/4-104=0

We multiply all the terms by the denominator


x^2*4+x*4+x-104*4=0

We add all the numbers together, and all the variables

x^2*4+x+x*4-416=0

Wy multiply elements

4x^2+x+4x-416=0

We add all the numbers together, and all the variables

4x^2+5x-416=0

a = 4; b = 5; c = -416;
Δ = b2-4ac
Δ = 52-4·4·(-416)
Δ = 6681
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-\sqrt{6681}}{2*4}=\frac{-5-\sqrt{6681}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+\sqrt{6681}}{2*4}=\frac{-5+\sqrt{6681}}{8}
$