2x+x^2/4=12

Solution for 2x+x^2/4=12 equation:

2x+x^2/4=12

We move all terms to the left:

2x+x^2/4-(12)=0

We multiply all the terms by the denominator


x^2+2x*4-12*4=0

We add all the numbers together, and all the variables

x^2+2x*4-48=0

Wy multiply elements

x^2+8x-48=0

a = 1; b = 8; c = -48;
Δ = b2-4ac
Δ = 82-4·1·(-48)
Δ = 256
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{256}=16$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-16}{2*1}=\frac{-24}{2}
=-12
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+16}{2*1}=\frac{8}{2}
=4
$