x(-17x-3)=-66

Solution for x(-17x-3)=-66 equation:

x(-17x-3)=-66

We move all terms to the left:

x(-17x-3)-(-66)=0

We add all the numbers together, and all the variables

x(-17x-3)+66=0

We multiply parentheses

-17x^2-3x+66=0

a = -17; b = -3; c = +66;
Δ = b2-4ac
Δ = -32-4·(-17)·66
Δ = 4497
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{-(-3)-\sqrt{4497}}{2*-17}=\frac{3-\sqrt{4497}}{-34}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+\sqrt{4497}}{2*-17}=\frac{3+\sqrt{4497}}{-34}
$