F(x)=2/5x-8

Solution for F(x)=2/5x-8 equation:

(F)=2/5F-8

We move all terms to the left:

(F)-(2/5F-8)=0


Domain of the equation: 5F-8)!=0

F∈R


We get rid of parentheses

F-2/5F+8=0

We multiply all the terms by the denominator


F*5F+8*5F-2=0

Wy multiply elements

5F^2+40F-2=0

a = 5; b = 40; c = -2;
Δ = b2-4ac
Δ = 402-4·5·(-2)
Δ = 1640
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:

$\sqrt{\Delta}=\sqrt{1640}=\sqrt{4*410}=\sqrt{4}*\sqrt{410}=2\sqrt{410}$
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(40)-2\sqrt{410}}{2*5}=\frac{-40-2\sqrt{410}}{10}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(40)+2\sqrt{410}}{2*5}=\frac{-40+2\sqrt{410}}{10}
$