F(x)=7x^2-28x-5

Solution for F(x)=7x^2-28x-5 equation:

(F)=7F^2-28F-5

We move all terms to the left:

(F)-(7F^2-28F-5)=0

We get rid of parentheses

-7F^2+F+28F+5=0

We add all the numbers together, and all the variables

-7F^2+29F+5=0

a = -7; b = 29; c = +5;
Δ = b2-4ac
Δ = 292-4·(-7)·5
Δ = 981
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:

$\sqrt{\Delta}=\sqrt{981}=\sqrt{9*109}=\sqrt{9}*\sqrt{109}=3\sqrt{109}$
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(29)-3\sqrt{109}}{2*-7}=\frac{-29-3\sqrt{109}}{-14}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(29)+3\sqrt{109}}{2*-7}=\frac{-29+3\sqrt{109}}{-14}
$