0.1x+100x=x^2/200

Solution for 0.1x+100x=x^2/200 equation:

0.1x+100x=x^2/200

We move all terms to the left:

0.1x+100x-(x^2/200)=0

We add all the numbers together, and all the variables

100.1x-(x^2/200)=0

We get rid of parentheses

-x^2/200+100.1x=0

We multiply all the terms by the denominator


-x^2+(100.1x)*200=0

We add all the numbers together, and all the variables

-x^2+(+100.1x)*200=0

We add all the numbers together, and all the variables

-1x^2+(+100.1x)*200=0

We multiply parentheses

-1x^2+20000x=0

a = -1; b = 20000; c = 0;
Δ = b2-4ac
Δ = 200002-4·(-1)·0
Δ = 400000000
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{400000000}=20000$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(20000)-20000}{2*-1}=\frac{-40000}{-2}
=+20000
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(20000)+20000}{2*-1}=\frac{0}{-2}
=0
$