-2x^2+14-9=-x^2+9x-5

Solution for -2x^2+14-9=-x^2+9x-5 equation:

-2x^2+14-9=-x^2+9x-5

We move all terms to the left:

-2x^2+14-9-(-x^2+9x-5)=0

We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

-1x^2-9x+10=0

a = -1; b = -9; c = +10;
Δ = b2-4ac
Δ = -92-4·(-1)·10
Δ = 121
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{121}=11$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-9)-11}{2*-1}=\frac{-2}{-2}
=1
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+11}{2*-1}=\frac{20}{-2}
=-10
$