-x^2+12x-21=0

Solution for -x^2+12x-21=0 equation:

-x^2+12x-21=0

We add all the numbers together, and all the variables

-1x^2+12x-21=0

a = -1; b = 12; c = -21;
Δ = b2-4ac
Δ = 122-4·(-1)·(-21)
Δ = 60
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{60}=\sqrt{4*15}=\sqrt{4}*\sqrt{15}=2\sqrt{15}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-2\sqrt{15}}{2*-1}=\frac{-12-2\sqrt{15}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+2\sqrt{15}}{2*-1}=\frac{-12+2\sqrt{15}}{-2}
$