-2x^2-9x=-4

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

-2x^2-9x=-4

We move all terms to the left:

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

We add all the numbers together, and all the variables

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

a = -2; b = -9; c = +4;
Δ = b2-4ac
Δ = -92-4·(-2)·4
Δ = 113
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{113}}{2*-2}=\frac{9-\sqrt{113}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+\sqrt{113}}{2*-2}=\frac{9+\sqrt{113}}{-4}
$