F(x)=5x2-7x-1

Solution for F(x)=5x2-7x-1 equation:

(F)=5F^2-7F-1

We move all terms to the left:

(F)-(5F^2-7F-1)=0

We get rid of parentheses

-5F^2+F+7F+1=0

We add all the numbers together, and all the variables

-5F^2+8F+1=0

a = -5; b = 8; c = +1;
Δ = b2-4ac
Δ = 82-4·(-5)·1
Δ = 84
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{84}=\sqrt{4*21}=\sqrt{4}*\sqrt{21}=2\sqrt{21}$
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-2\sqrt{21}}{2*-5}=\frac{-8-2\sqrt{21}}{-10}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+2\sqrt{21}}{2*-5}=\frac{-8+2\sqrt{21}}{-10}
$