7500/x+100=0.02x^2

Solution for 7500/x+100=0.02x^2 equation:

7500/x+100=0.02x^2

We move all terms to the left:

7500/x+100-(0.02x^2)=0


Domain of the equation: x!=0

x∈R


We get rid of parentheses

-0.02x^2+7500/x+100=0

We multiply all the terms by the denominator


-(0.02x^2)*x+100*x+7500=0

We add all the numbers together, and all the variables

100x-(0.02x^2)*x+7500=0

We multiply parentheses

-0x^2+100x+7500=0

We add all the numbers together, and all the variables

-1x^2+100x+7500=0

a = -1; b = 100; c = +7500;
Δ = b2-4ac
Δ = 1002-4·(-1)·7500
Δ = 40000
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{40000}=200$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(100)-200}{2*-1}=\frac{-300}{-2}
=+150
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(100)+200}{2*-1}=\frac{100}{-2}
=-50
$