0.497=x^2/1.66-x

Solution for 0.497=x^2/1.66-x equation:

0.497=x^2/1.66-x

We move all terms to the left:

0.497-(x^2/1.66-x)=0


Domain of the equation: 1.66-x)!=0

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

-x)!=-1.66

x!=-1.66/1

x!=-1.66

x∈R


We get rid of parentheses

-x^2/1.66+x+0.497=0

We multiply all the terms by the denominator


-x^2+x*1.66+(0.497)*1.66=0

We add all the numbers together, and all the variables

-1x^2+x*1.66+0.82502=0

Wy multiply elements

-1x^2+1.66x+0.82502=0

a = -1; b = 1.66; c = +0.82502;
Δ = b2-4ac
Δ = 1.662-4·(-1)·0.82502
Δ = 6.05568
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{-(1.66)-\sqrt{6.05568}}{2*-1}=\frac{-1.66-\sqrt{6.05568}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1.66)+\sqrt{6.05568}}{2*-1}=\frac{-1.66+\sqrt{6.05568}}{-2}
$