x^2+x/4-20=0

Solution for x^2+x/4-20=0 equation:

x^2+x/4-20=0

We multiply all the terms by the denominator


x^2*4+x-20*4=0

We add all the numbers together, and all the variables

x^2*4+x-80=0

Wy multiply elements

4x^2+x-80=0

a = 4; b = 1; c = -80;
Δ = b2-4ac
Δ = 12-4·4·(-80)
Δ = 1281
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{-(1)-\sqrt{1281}}{2*4}=\frac{-1-\sqrt{1281}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+\sqrt{1281}}{2*4}=\frac{-1+\sqrt{1281}}{8}
$