F(x)=-5/8x+16

Solution for F(x)=-5/8x+16 equation:

(F)=-5/8F+16

We move all terms to the left:

(F)-(-5/8F+16)=0


Domain of the equation: 8F+16)!=0

F∈R


We get rid of parentheses

F+5/8F-16=0

We multiply all the terms by the denominator


F*8F-16*8F+5=0

Wy multiply elements

8F^2-128F+5=0

a = 8; b = -128; c = +5;
Δ = b2-4ac
Δ = -1282-4·8·5
Δ = 16224
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:

$\sqrt{\Delta}=\sqrt{16224}=\sqrt{2704*6}=\sqrt{2704}*\sqrt{6}=52\sqrt{6}$
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-128)-52\sqrt{6}}{2*8}=\frac{128-52\sqrt{6}}{16}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-128)+52\sqrt{6}}{2*8}=\frac{128+52\sqrt{6}}{16}
$