F(x)=8x-2/7x-8

Solution for F(x)=8x-2/7x-8 equation:

(F)=8F-2/7F-8

We move all terms to the left:

(F)-(8F-2/7F-8)=0


Domain of the equation: 7F-8)!=0

F∈R


We get rid of parentheses

F-8F+2/7F+8=0

We multiply all the terms by the denominator


F*7F-8F*7F+8*7F+2=0

Wy multiply elements

7F^2-56F^2+56F+2=0

We add all the numbers together, and all the variables

-49F^2+56F+2=0

a = -49; b = 56; c = +2;
Δ = b2-4ac
Δ = 562-4·(-49)·2
Δ = 3528
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:

$\sqrt{\Delta}=\sqrt{3528}=\sqrt{1764*2}=\sqrt{1764}*\sqrt{2}=42\sqrt{2}$
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(56)-42\sqrt{2}}{2*-49}=\frac{-56-42\sqrt{2}}{-98}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(56)+42\sqrt{2}}{2*-49}=\frac{-56+42\sqrt{2}}{-98}
$