F(x)=-3/5x+2

Solution for F(x)=-3/5x+2 equation:

(F)=-3/5F+2

We move all terms to the left:

(F)-(-3/5F+2)=0


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

F∈R


We get rid of parentheses

F+3/5F-2=0

We multiply all the terms by the denominator


F*5F-2*5F+3=0

Wy multiply elements

5F^2-10F+3=0

a = 5; b = -10; c = +3;
Δ = b2-4ac
Δ = -102-4·5·3
Δ = 40
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:

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