F(x)=15x^2+3x-10

Solution for F(x)=15x^2+3x-10 equation:

(F)=15F^2+3F-10

We move all terms to the left:

(F)-(15F^2+3F-10)=0

We get rid of parentheses

-15F^2+F-3F+10=0

We add all the numbers together, and all the variables

-15F^2-2F+10=0

a = -15; b = -2; c = +10;
Δ = b2-4ac
Δ = -22-4·(-15)·10
Δ = 604
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:

$\sqrt{\Delta}=\sqrt{604}=\sqrt{4*151}=\sqrt{4}*\sqrt{151}=2\sqrt{151}$
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-2\sqrt{151}}{2*-15}=\frac{2-2\sqrt{151}}{-30}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+2\sqrt{151}}{2*-15}=\frac{2+2\sqrt{151}}{-30}
$