-9x=5x^2-1

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

-9x=5x^2-1

We move all terms to the left:

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

We get rid of parentheses

-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}
$