.89=x-7/x

Solution for .89=x-7/x equation:

.89=x-7/x

We move all terms to the left:

.89-(x-7/x)=0


Domain of the equation: x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

-(+x-7/x)+.89=0

We add all the numbers together, and all the variables

-(+x-7/x)+0.89=0

We get rid of parentheses

-x+7/x+0.89=0

We multiply all the terms by the denominator


-x*x+(0.89)*x+7=0

We multiply parentheses

-x*x+0.89x+7=0

Wy multiply elements

-1x^2+0.89x+7=0

a = -1; b = 0.89; c = +7;
Δ = b2-4ac
Δ = 0.892-4·(-1)·7
Δ = 28.7921
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{-(0.89)-\sqrt{28.7921}}{2*-1}=\frac{-0.89-\sqrt{28.7921}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0.89)+\sqrt{28.7921}}{2*-1}=\frac{-0.89+\sqrt{28.7921}}{-2}
$