F(x)=-2/5x+4

Solution for F(x)=-2/5x+4 equation:

(F)=-2/5F+4

We move all terms to the left:

(F)-(-2/5F+4)=0


Domain of the equation: 5F+4)!=0

F∈R


We get rid of parentheses

F+2/5F-4=0

We multiply all the terms by the denominator


F*5F-4*5F+2=0

Wy multiply elements

5F^2-20F+2=0

a = 5; b = -20; c = +2;
Δ = b2-4ac
Δ = -202-4·5·2
Δ = 360
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:

$\sqrt{\Delta}=\sqrt{360}=\sqrt{36*10}=\sqrt{36}*\sqrt{10}=6\sqrt{10}$
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-20)-6\sqrt{10}}{2*5}=\frac{20-6\sqrt{10}}{10}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-20)+6\sqrt{10}}{2*5}=\frac{20+6\sqrt{10}}{10}
$