F(x)=4/5x+4

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

(F)=4/5F+4

We move all terms to the left:

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


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

F∈R


We get rid of parentheses

F-4/5F-4=0

We multiply all the terms by the denominator


F*5F-4*5F-4=0

Wy multiply elements

5F^2-20F-4=0

a = 5; b = -20; c = -4;
Δ = b2-4ac
Δ = -202-4·5·(-4)
Δ = 480
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:

$\sqrt{\Delta}=\sqrt{480}=\sqrt{16*30}=\sqrt{16}*\sqrt{30}=4\sqrt{30}$
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-20)-4\sqrt{30}}{2*5}=\frac{20-4\sqrt{30}}{10}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-20)+4\sqrt{30}}{2*5}=\frac{20+4\sqrt{30}}{10}
$