F(x)=8/7x-8

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

(F)=8/7F-8

We move all terms to the left:

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


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

F∈R


We get rid of parentheses

F-8/7F+8=0

We multiply all the terms by the denominator


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

Wy multiply elements

7F^2+56F-8=0

a = 7; b = 56; c = -8;
Δ = b2-4ac
Δ = 562-4·7·(-8)
Δ = 3360
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:

$\sqrt{\Delta}=\sqrt{3360}=\sqrt{16*210}=\sqrt{16}*\sqrt{210}=4\sqrt{210}$
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(56)-4\sqrt{210}}{2*7}=\frac{-56-4\sqrt{210}}{14}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(56)+4\sqrt{210}}{2*7}=\frac{-56+4\sqrt{210}}{14}
$