x^2+x/4=147

Solution for x^2+x/4=147 equation:

x^2+x/4=147

We move all terms to the left:

x^2+x/4-(147)=0

We multiply all the terms by the denominator


x^2*4+x-147*4=0

We add all the numbers together, and all the variables

x^2*4+x-588=0

Wy multiply elements

4x^2+x-588=0

a = 4; b = 1; c = -588;
Δ = b2-4ac
Δ = 12-4·4·(-588)
Δ = 9409
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{9409}=97$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-97}{2*4}=\frac{-98}{8}
=-12+1/4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+97}{2*4}=\frac{96}{8}
=12
$