F(x)=-2x^2+96x-270

Solution for F(x)=-2x^2+96x-270 equation:

(F)=-2F^2+96F-270

We move all terms to the left:

(F)-(-2F^2+96F-270)=0

We get rid of parentheses

2F^2-96F+F+270=0

We add all the numbers together, and all the variables

2F^2-95F+270=0

a = 2; b = -95; c = +270;
Δ = b2-4ac
Δ = -952-4·2·270
Δ = 6865
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-95)-\sqrt{6865}}{2*2}=\frac{95-\sqrt{6865}}{4}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-95)+\sqrt{6865}}{2*2}=\frac{95+\sqrt{6865}}{4}
$