-5x^2-9x=-1

Solution for -5x^2-9x=-1 equation:

-5x^2-9x=-1

We move all terms to the left:

-5x^2-9x-(-1)=0

We add all the numbers together, and all the variables

-5x^2-9x+1=0

a = -5; b = -9; c = +1;
Δ = b2-4ac
Δ = -92-4·(-5)·1
Δ = 101
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{-(-9)-\sqrt{101}}{2*-5}=\frac{9-\sqrt{101}}{-10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+\sqrt{101}}{2*-5}=\frac{9+\sqrt{101}}{-10}
$