F(x)=5x^2-2x-10

Solution for F(x)=5x^2-2x-10 equation:

(F)=5F^2-2F-10

We move all terms to the left:

(F)-(5F^2-2F-10)=0

We get rid of parentheses

-5F^2+F+2F+10=0

We add all the numbers together, and all the variables

-5F^2+3F+10=0

a = -5; b = 3; c = +10;
Δ = b2-4ac
Δ = 32-4·(-5)·10
Δ = 209
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{-(3)-\sqrt{209}}{2*-5}=\frac{-3-\sqrt{209}}{-10}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+\sqrt{209}}{2*-5}=\frac{-3+\sqrt{209}}{-10}
$