-a2+19a-90=0

Solution for -a2+19a-90=0 equation:

-a2+19a-90=0

We add all the numbers together, and all the variables

-1a^2+19a-90=0

a = -1; b = 19; c = -90;
Δ = b2-4ac
Δ = 192-4·(-1)·(-90)
Δ = 1
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1}=1$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(19)-1}{2*-1}=\frac{-20}{-2}
=+10
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(19)+1}{2*-1}=\frac{-18}{-2}
=+9
$