-x2+29x-180=0

Solution for -x2+29x-180=0 equation:

-x2+29x-180=0

We add all the numbers together, and all the variables

-1x^2+29x-180=0

a = -1; b = 29; c = -180;
Δ = b2-4ac
Δ = 292-4·(-1)·(-180)
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{-(29)-11}{2*-1}=\frac{-40}{-2}
=+20
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(29)+11}{2*-1}=\frac{-18}{-2}
=+9
$