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

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

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

We move all terms to the left:

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

-5F^2-6F+3=0

a = -5; b = -6; c = +3;
Δ = b2-4ac
Δ = -62-4·(-5)·3
Δ = 96
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:

$\sqrt{\Delta}=\sqrt{96}=\sqrt{16*6}=\sqrt{16}*\sqrt{6}=4\sqrt{6}$
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-4\sqrt{6}}{2*-5}=\frac{6-4\sqrt{6}}{-10}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+4\sqrt{6}}{2*-5}=\frac{6+4\sqrt{6}}{-10}
$