F(x)=-5/8x+14

Solution for F(x)=-5/8x+14 equation:

(F)=-5/8F+14

We move all terms to the left:

(F)-(-5/8F+14)=0


Domain of the equation: 8F+14)!=0

F∈R


We get rid of parentheses

F+5/8F-14=0

We multiply all the terms by the denominator


F*8F-14*8F+5=0

Wy multiply elements

8F^2-112F+5=0

a = 8; b = -112; c = +5;
Δ = b2-4ac
Δ = -1122-4·8·5
Δ = 12384
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:

$\sqrt{\Delta}=\sqrt{12384}=\sqrt{144*86}=\sqrt{144}*\sqrt{86}=12\sqrt{86}$
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-112)-12\sqrt{86}}{2*8}=\frac{112-12\sqrt{86}}{16}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-112)+12\sqrt{86}}{2*8}=\frac{112+12\sqrt{86}}{16}
$