-2x^2+45=-x

Solution for -2x^2+45=-x equation:

-2x^2+45=-x

We move all terms to the left:

-2x^2+45-(-x)=0

We add all the numbers together, and all the variables

-2x^2-(-1x)+45=0

We get rid of parentheses

-2x^2+1x+45=0

We add all the numbers together, and all the variables

-2x^2+x+45=0

a = -2; b = 1; c = +45;
Δ = b2-4ac
Δ = 12-4·(-2)·45
Δ = 361
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{361}=19$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-19}{2*-2}=\frac{-20}{-4}
=+5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+19}{2*-2}=\frac{18}{-4}
=-4+1/2
$