F(x)=8/6x-2

Solution for F(x)=8/6x-2 equation:

(F)=8/6F-2

We move all terms to the left:

(F)-(8/6F-2)=0


Domain of the equation: 6F-2)!=0

F∈R


We get rid of parentheses

F-8/6F+2=0

We multiply all the terms by the denominator


F*6F+2*6F-8=0

Wy multiply elements

6F^2+12F-8=0

a = 6; b = 12; c = -8;
Δ = b2-4ac
Δ = 122-4·6·(-8)
Δ = 336
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:

$\sqrt{\Delta}=\sqrt{336}=\sqrt{16*21}=\sqrt{16}*\sqrt{21}=4\sqrt{21}$
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-4\sqrt{21}}{2*6}=\frac{-12-4\sqrt{21}}{12}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+4\sqrt{21}}{2*6}=\frac{-12+4\sqrt{21}}{12}
$