x+x^2/4=0.05

Solution for x+x^2/4=0.05 equation:

x+x^2/4=0.05

We move all terms to the left:

x+x^2/4-(0.05)=0

We add all the numbers together, and all the variables

x^2/4+x-0.05=0

We multiply all the terms by the denominator


x^2+x*4-(0.05)*4=0

We add all the numbers together, and all the variables

x^2+x*4-0.2=0

Wy multiply elements

x^2+4x-0.2=0

a = 1; b = 4; c = -0.2;
Δ = b2-4ac
Δ = 42-4·1·(-0.2)
Δ = 16.8
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{-(4)-\sqrt{16.8}}{2*1}=\frac{-4-\sqrt{16.8}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+\sqrt{16.8}}{2*1}=\frac{-4+\sqrt{16.8}}{2}
$