F(1)=5(1)x2/19

Solution for F(1)=5(1)x2/19 equation:

(1)=5(1)F2/19

We move all terms to the left:

(1)-(5(1)F2/19)=0

We add all the numbers together, and all the variables

-(+51F2/19)+1=0

We get rid of parentheses

-51F2/19+1=0

We multiply all the terms by the denominator


-51F2+1*19=0

We add all the numbers together, and all the variables

-51F^2+19=0

a = -51; b = 0; c = +19;
Δ = b2-4ac
Δ = 02-4·(-51)·19
Δ = 3876
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:

$\sqrt{\Delta}=\sqrt{3876}=\sqrt{4*969}=\sqrt{4}*\sqrt{969}=2\sqrt{969}$
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{969}}{2*-51}=\frac{0-2\sqrt{969}}{-102}
=-\frac{2\sqrt{969}}{-102}
=-\frac{\sqrt{969}}{-51}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{969}}{2*-51}=\frac{0+2\sqrt{969}}{-102}
=\frac{2\sqrt{969}}{-102}
=\frac{\sqrt{969}}{-51}
$