F(x)=9x^2+5x-8

Solution for F(x)=9x^2+5x-8 equation:

(F)=9F^2+5F-8

We move all terms to the left:

(F)-(9F^2+5F-8)=0

We get rid of parentheses

-9F^2+F-5F+8=0

We add all the numbers together, and all the variables

-9F^2-4F+8=0

a = -9; b = -4; c = +8;
Δ = b2-4ac
Δ = -42-4·(-9)·8
Δ = 304
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:

$\sqrt{\Delta}=\sqrt{304}=\sqrt{16*19}=\sqrt{16}*\sqrt{19}=4\sqrt{19}$
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-4\sqrt{19}}{2*-9}=\frac{4-4\sqrt{19}}{-18}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+4\sqrt{19}}{2*-9}=\frac{4+4\sqrt{19}}{-18}
$