F(x)=8x^2+22x-21

Solution for F(x)=8x^2+22x-21 equation:

(F)=8F^2+22F-21

We move all terms to the left:

(F)-(8F^2+22F-21)=0

We get rid of parentheses

-8F^2+F-22F+21=0

We add all the numbers together, and all the variables

-8F^2-21F+21=0

a = -8; b = -21; c = +21;
Δ = b2-4ac
Δ = -212-4·(-8)·21
Δ = 1113
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-21)-\sqrt{1113}}{2*-8}=\frac{21-\sqrt{1113}}{-16}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-21)+\sqrt{1113}}{2*-8}=\frac{21+\sqrt{1113}}{-16}
$