66.67-3.34x^2=1.645x=0

Solution for 66.67-3.34x^2=1.645x=0 equation:

66.67-3.34x^2=1.645x=0

We move all terms to the left:

66.67-3.34x^2-(1.645x)=0

We add all the numbers together, and all the variables

-3.34x^2-(+1.645x)+66.67=0

We get rid of parentheses

-3.34x^2-1.645x+66.67=0

a = -3.34; b = -1.645; c = +66.67;
Δ = b2-4ac
Δ = -1.6452-4·(-3.34)·66.67
Δ = 893.417225
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{-(-1.645)-\sqrt{893.417225}}{2*-3.34}=\frac{1.645-\sqrt{893.417225}}{-6.68}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1.645)+\sqrt{893.417225}}{2*-3.34}=\frac{1.645+\sqrt{893.417225}}{-6.68}
$