9009=67x^2+55x+6

Solution for 9009=67x^2+55x+6 equation:

9009=67x^2+55x+6

We move all terms to the left:

9009-(67x^2+55x+6)=0

We get rid of parentheses

-67x^2-55x-6+9009=0

We add all the numbers together, and all the variables

-67x^2-55x+9003=0

a = -67; b = -55; c = +9003;
Δ = b2-4ac
Δ = -552-4·(-67)·9003
Δ = 2415829
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{-(-55)-\sqrt{2415829}}{2*-67}=\frac{55-\sqrt{2415829}}{-134}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-55)+\sqrt{2415829}}{2*-67}=\frac{55+\sqrt{2415829}}{-134}
$