x^2+x/4=260

Solution for x^2+x/4=260 equation:

x^2+x/4=260

We move all terms to the left:

x^2+x/4-(260)=0

We multiply all the terms by the denominator


x^2*4+x-260*4=0

We add all the numbers together, and all the variables

x^2*4+x-1040=0

Wy multiply elements

4x^2+x-1040=0

a = 4; b = 1; c = -1040;
Δ = b2-4ac
Δ = 12-4·4·(-1040)
Δ = 16641
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{16641}=129$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-129}{2*4}=\frac{-130}{8}
=-16+1/4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+129}{2*4}=\frac{128}{8}
=16
$