F(x)=1/8x-11

Solution for F(x)=1/8x-11 equation:

(F)=1/8F-11

We move all terms to the left:

(F)-(1/8F-11)=0


Domain of the equation: 8F-11)!=0

F∈R


We get rid of parentheses

F-1/8F+11=0

We multiply all the terms by the denominator


F*8F+11*8F-1=0

Wy multiply elements

8F^2+88F-1=0

a = 8; b = 88; c = -1;
Δ = b2-4ac
Δ = 882-4·8·(-1)
Δ = 7776
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:

$\sqrt{\Delta}=\sqrt{7776}=\sqrt{1296*6}=\sqrt{1296}*\sqrt{6}=36\sqrt{6}$
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(88)-36\sqrt{6}}{2*8}=\frac{-88-36\sqrt{6}}{16}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(88)+36\sqrt{6}}{2*8}=\frac{-88+36\sqrt{6}}{16}
$