F(x)=5.23X^2-4.84X-1.91

Solution for F(x)=5.23X^2-4.84X-1.91 equation:

(F)=5.23F^2-4.84F-1.91

We move all terms to the left:

(F)-(5.23F^2-4.84F-1.91)=0

We get rid of parentheses

-5.23F^2+F+4.84F+1.91=0

We add all the numbers together, and all the variables

-5.23F^2+5.84F+1.91=0

a = -5.23; b = 5.84; c = +1.91;
Δ = b2-4ac
Δ = 5.842-4·(-5.23)·1.91
Δ = 74.0628
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{-(5.84)-\sqrt{74.0628}}{2*-5.23}=\frac{-5.84-\sqrt{74.0628}}{-10.46}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5.84)+\sqrt{74.0628}}{2*-5.23}=\frac{-5.84+\sqrt{74.0628}}{-10.46}
$