F(w)=15w^2-13w+2

Solution for F(w)=15w^2-13w+2 equation:

(F)=15F^2-13F+2

We move all terms to the left:

(F)-(15F^2-13F+2)=0

We get rid of parentheses

-15F^2+F+13F-2=0

We add all the numbers together, and all the variables

-15F^2+14F-2=0

a = -15; b = 14; c = -2;
Δ = b2-4ac
Δ = 142-4·(-15)·(-2)
Δ = 76
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:

$\sqrt{\Delta}=\sqrt{76}=\sqrt{4*19}=\sqrt{4}*\sqrt{19}=2\sqrt{19}$
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(14)-2\sqrt{19}}{2*-15}=\frac{-14-2\sqrt{19}}{-30}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(14)+2\sqrt{19}}{2*-15}=\frac{-14+2\sqrt{19}}{-30}
$