F(x)=1/2x-20

Solution for F(x)=1/2x-20 equation:

(F)=1/2F-20

We move all terms to the left:

(F)-(1/2F-20)=0


Domain of the equation: 2F-20)!=0

F∈R


We get rid of parentheses

F-1/2F+20=0

We multiply all the terms by the denominator


F*2F+20*2F-1=0

Wy multiply elements

2F^2+40F-1=0

a = 2; b = 40; c = -1;
Δ = b2-4ac
Δ = 402-4·2·(-1)
Δ = 1608
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:

$\sqrt{\Delta}=\sqrt{1608}=\sqrt{4*402}=\sqrt{4}*\sqrt{402}=2\sqrt{402}$
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(40)-2\sqrt{402}}{2*2}=\frac{-40-2\sqrt{402}}{4}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(40)+2\sqrt{402}}{2*2}=\frac{-40+2\sqrt{402}}{4}
$