-4x^2-5=-9x

Solution for -4x^2-5=-9x equation:

-4x^2-5=-9x

We move all terms to the left:

-4x^2-5-(-9x)=0

We get rid of parentheses

-4x^2+9x-5=0

a = -4; b = 9; c = -5;
Δ = b2-4ac
Δ = 92-4·(-4)·(-5)
Δ = 1
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1}=1$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(9)-1}{2*-4}=\frac{-10}{-8}
=1+1/4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+1}{2*-4}=\frac{-8}{-8}
=1
$