8.9(10^-7)=x^2/0.10-x

Solution for 8.9(10^-7)=x^2/0.10-x equation:

8.9(10^-7)=x^2/0.10-x

We move all terms to the left:

8.9(10^-7)-(x^2/0.10-x)=0


Domain of the equation: 0.10-x)!=0

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

-x)!=-0.10

x!=-0.10/1

x!=-0.10

x∈R


We add all the numbers together, and all the variables

-(x^2/0.10-x)-7+8.9E=0

We get rid of parentheses

-x^2/0.10+x-7+8.9E=0

We multiply all the terms by the denominator


-x^2+x*0.10-7*0.10+(8.9E)*0.10=0

We add all the numbers together, and all the variables

-x^2+x*0.10-7*0.10+(24.192708273286)*0.10=0

We add all the numbers together, and all the variables

-1x^2+x*0.10+1.7192708273286=0

Wy multiply elements

-1x^2+0.1x+1.7192708273286=0

a = -1; b = 0.1; c = +1.7192708273286;
Δ = b2-4ac
Δ = 0.12-4·(-1)·1.7192708273286
Δ = 6.8870833093144
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{-(0.1)-\sqrt{6.8870833093144}}{2*-1}=\frac{-0.1-\sqrt{6.8870833093144}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0.1)+\sqrt{6.8870833093144}}{2*-1}=\frac{-0.1+\sqrt{6.8870833093144}}{-2}
$