F(x)=-6X^2+8-3x

Solution for F(x)=-6X^2+8-3x equation:

(F)=-6F^2+8-3F

We move all terms to the left:

(F)-(-6F^2+8-3F)=0

We get rid of parentheses

6F^2+3F+F-8=0

We add all the numbers together, and all the variables

6F^2+4F-8=0

a = 6; b = 4; c = -8;
Δ = b2-4ac
Δ = 42-4·6·(-8)
Δ = 208
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:

$\sqrt{\Delta}=\sqrt{208}=\sqrt{16*13}=\sqrt{16}*\sqrt{13}=4\sqrt{13}$
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-4\sqrt{13}}{2*6}=\frac{-4-4\sqrt{13}}{12}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+4\sqrt{13}}{2*6}=\frac{-4+4\sqrt{13}}{12}
$