0.20=x^2/85-x

Solution for 0.20=x^2/85-x equation:

0.20=x^2/85-x

We move all terms to the left:

0.20-(x^2/85-x)=0


Domain of the equation: 85-x)!=0

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

-x)!=-85

x!=-85/1

x!=-85

x∈R


We add all the numbers together, and all the variables

-(x^2/85-x)+0.2=0

We get rid of parentheses

-x^2/85+x+0.2=0

We multiply all the terms by the denominator


-x^2+x*85+(0.2)*85=0

We add all the numbers together, and all the variables

-1x^2+x*85+17=0

Wy multiply elements

-1x^2+85x+17=0

a = -1; b = 85; c = +17;
Δ = b2-4ac
Δ = 852-4·(-1)·17
Δ = 7293
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{-(85)-\sqrt{7293}}{2*-1}=\frac{-85-\sqrt{7293}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(85)+\sqrt{7293}}{2*-1}=\frac{-85+\sqrt{7293}}{-2}
$