164/9=x2-x

Solution for 164/9=x2-x equation:

164/9=x2-x

We move all terms to the left:

164/9-(x2-x)=0

We add all the numbers together, and all the variables

-(+x^2-1x)+164/9=0

We get rid of parentheses

-x^2+1x+164/9=0

We multiply all the terms by the denominator


-x^2*9+1x*9+164=0

Wy multiply elements

-9x^2+9x+164=0

a = -9; b = 9; c = +164;
Δ = b2-4ac
Δ = 92-4·(-9)·164
Δ = 5985
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{5985}=\sqrt{9*665}=\sqrt{9}*\sqrt{665}=3\sqrt{665}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(9)-3\sqrt{665}}{2*-9}=\frac{-9-3\sqrt{665}}{-18}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+3\sqrt{665}}{2*-9}=\frac{-9+3\sqrt{665}}{-18}
$