F(x)=3x2+7x-3

Solution for F(x)=3x2+7x-3 equation:

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

We move all terms to the left:

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

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

a = -3; b = -6; c = +3;
Δ = b2-4ac
Δ = -62-4·(-3)·3
Δ = 72
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:

$\sqrt{\Delta}=\sqrt{72}=\sqrt{36*2}=\sqrt{36}*\sqrt{2}=6\sqrt{2}$
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-6\sqrt{2}}{2*-3}=\frac{6-6\sqrt{2}}{-6}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+6\sqrt{2}}{2*-3}=\frac{6+6\sqrt{2}}{-6}
$