F(6)=x2-4/20

Solution for F(6)=x2-4/20 equation:

(6)=F2-4/20

We move all terms to the left:

(6)-(F2-4/20)=0

We add all the numbers together, and all the variables

-(+F^2-4/20)+6=0

We get rid of parentheses

-F^2+6+4/20=0

We multiply all the terms by the denominator


-F^2*20+4+6*20=0

We add all the numbers together, and all the variables

-F^2*20+124=0

Wy multiply elements

-20F^2+124=0

a = -20; b = 0; c = +124;
Δ = b2-4ac
Δ = 02-4·(-20)·124
Δ = 9920
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:

$\sqrt{\Delta}=\sqrt{9920}=\sqrt{64*155}=\sqrt{64}*\sqrt{155}=8\sqrt{155}$
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-8\sqrt{155}}{2*-20}=\frac{0-8\sqrt{155}}{-40}
=-\frac{8\sqrt{155}}{-40}
=-\frac{\sqrt{155}}{-5}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+8\sqrt{155}}{2*-20}=\frac{0+8\sqrt{155}}{-40}
=\frac{8\sqrt{155}}{-40}
=\frac{\sqrt{155}}{-5}
$