F(x)=7x^2+5x-3

Solution for F(x)=7x^2+5x-3 equation:

(F)=7F^2+5F-3

We move all terms to the left:

(F)-(7F^2+5F-3)=0

We get rid of parentheses

-7F^2+F-5F+3=0

We add all the numbers together, and all the variables

-7F^2-4F+3=0

a = -7; b = -4; c = +3;
Δ = b2-4ac
Δ = -42-4·(-7)·3
Δ = 100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{100}=10$
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-10}{2*-7}=\frac{-6}{-14}
=3/7
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+10}{2*-7}=\frac{14}{-14}
=-1
$