F(x)=-16x2+42x+10

Solution for F(x)=-16x2+42x+10 equation:

(F)=-16F^2+42F+10

We move all terms to the left:

(F)-(-16F^2+42F+10)=0

We get rid of parentheses

16F^2-42F+F-10=0

We add all the numbers together, and all the variables

16F^2-41F-10=0

a = 16; b = -41; c = -10;
Δ = b2-4ac
Δ = -412-4·16·(-10)
Δ = 2321
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{-(-41)-\sqrt{2321}}{2*16}=\frac{41-\sqrt{2321}}{32}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-41)+\sqrt{2321}}{2*16}=\frac{41+\sqrt{2321}}{32}
$