0.2=x^2/65-x

Solution for 0.2=x^2/65-x equation:

0.2=x^2/65-x

We move all terms to the left:

0.2-(x^2/65-x)=0


Domain of the equation: 65-x)!=0

We move all terms containing x to the left, all other terms to the right

-x)!=-65

x!=-65/1

x!=-65

x∈R


We get rid of parentheses

-x^2/65+x+0.2=0

We multiply all the terms by the denominator


-x^2+x*65+(0.2)*65=0

We add all the numbers together, and all the variables

-1x^2+x*65+13=0

Wy multiply elements

-1x^2+65x+13=0

a = -1; b = 65; c = +13;
Δ = b2-4ac
Δ = 652-4·(-1)·13
Δ = 4277
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{-(65)-\sqrt{4277}}{2*-1}=\frac{-65-\sqrt{4277}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(65)+\sqrt{4277}}{2*-1}=\frac{-65+\sqrt{4277}}{-2}
$