-x^2=3x-16

Solution for -x^2=3x-16 equation:

-x^2=3x-16

We move all terms to the left:

-x^2-(3x-16)=0

We add all the numbers together, and all the variables

-1x^2-(3x-16)=0

We get rid of parentheses

-1x^2-3x+16=0

a = -1; b = -3; c = +16;
Δ = b2-4ac
Δ = -32-4·(-1)·16
Δ = 73
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{-(-3)-\sqrt{73}}{2*-1}=\frac{3-\sqrt{73}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+\sqrt{73}}{2*-1}=\frac{3+\sqrt{73}}{-2}
$