F(x)=x^2+5x/1

Solution for F(x)=x^2+5x/1 equation:

(F)=F^2+5F/1

We move all terms to the left:

(F)-(F^2+5F/1)=0

We get rid of parentheses

-F^2+F-5F/1=0

We multiply all the terms by the denominator


-F^2*1+F*1-5F=0

We add all the numbers together, and all the variables

-F^2*1-5F+F*1=0

Wy multiply elements

-1F^2-5F+F=0

We add all the numbers together, and all the variables

-1F^2-4F=0

a = -1; b = -4; c = 0;
Δ = b2-4ac
Δ = -42-4·(-1)·0
Δ = 16
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{16}=4$
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-4}{2*-1}=\frac{0}{-2}
=0
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+4}{2*-1}=\frac{8}{-2}
=-4
$