F(x)=5/5x-2

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

(F)=5/5F-2

We move all terms to the left:

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


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

F∈R


We get rid of parentheses

F-5/5F+2=0

We multiply all the terms by the denominator


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

Wy multiply elements

5F^2+10F-5=0

a = 5; b = 10; c = -5;
Δ = b2-4ac
Δ = 102-4·5·(-5)
Δ = 200
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:

$\sqrt{\Delta}=\sqrt{200}=\sqrt{100*2}=\sqrt{100}*\sqrt{2}=10\sqrt{2}$
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-10\sqrt{2}}{2*5}=\frac{-10-10\sqrt{2}}{10}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+10\sqrt{2}}{2*5}=\frac{-10+10\sqrt{2}}{10}
$