I(x)=-x^2+40x-350

Solution for I(x)=-x^2+40x-350 equation:

(I)=-I^2+40I-350

We move all terms to the left:

(I)-(-I^2+40I-350)=0

We get rid of parentheses

I^2-40I+I+350=0

We add all the numbers together, and all the variables

I^2-39I+350=0

a = 1; b = -39; c = +350;
Δ = b2-4ac
Δ = -392-4·1·350
Δ = 121
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$I_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$I_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{121}=11$
$I_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-39)-11}{2*1}=\frac{28}{2}
=14
$
$I_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-39)+11}{2*1}=\frac{50}{2}
=25
$