x+(x^2)/20=75

Solution for x+(x^2)/20=75 equation:

x+(x^2)/20=75

We move all terms to the left:

x+(x^2)/20-(75)=0

determiningTheFunctionDomain
x^2/20+x-75=0

We multiply all the terms by the denominator


x^2+x*20-75*20=0

We add all the numbers together, and all the variables

x^2+x*20-1500=0

Wy multiply elements

x^2+20x-1500=0

a = 1; b = 20; c = -1500;
Δ = b2-4ac
Δ = 202-4·1·(-1500)
Δ = 6400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{6400}=80$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(20)-80}{2*1}=\frac{-100}{2}
=-50
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(20)+80}{2*1}=\frac{60}{2}
=30
$