F(x)=3x^2-17x+10

Solution for F(x)=3x^2-17x+10 equation:

(F)=3F^2-17F+10

We move all terms to the left:

(F)-(3F^2-17F+10)=0

We get rid of parentheses

-3F^2+F+17F-10=0

We add all the numbers together, and all the variables

-3F^2+18F-10=0

a = -3; b = 18; c = -10;
Δ = b2-4ac
Δ = 182-4·(-3)·(-10)
Δ = 204
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:

$\sqrt{\Delta}=\sqrt{204}=\sqrt{4*51}=\sqrt{4}*\sqrt{51}=2\sqrt{51}$
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(18)-2\sqrt{51}}{2*-3}=\frac{-18-2\sqrt{51}}{-6}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(18)+2\sqrt{51}}{2*-3}=\frac{-18+2\sqrt{51}}{-6}
$