F(x)=4/5x+2

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

(F)=4/5F+2

We move all terms to the left:

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


Domain of the equation: 5F+2)!=0

F∈R


We get rid of parentheses

F-4/5F-2=0

We multiply all the terms by the denominator


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

Wy multiply elements

5F^2-10F-4=0

a = 5; b = -10; c = -4;
Δ = b2-4ac
Δ = -102-4·5·(-4)
Δ = 180
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:

$\sqrt{\Delta}=\sqrt{180}=\sqrt{36*5}=\sqrt{36}*\sqrt{5}=6\sqrt{5}$
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-6\sqrt{5}}{2*5}=\frac{10-6\sqrt{5}}{10}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+6\sqrt{5}}{2*5}=\frac{10+6\sqrt{5}}{10}
$