F(x)=8/7x-4

Solution for F(x)=8/7x-4 equation:

(F)=8/7F-4

We move all terms to the left:

(F)-(8/7F-4)=0


Domain of the equation: 7F-4)!=0

F∈R


We get rid of parentheses

F-8/7F+4=0

We multiply all the terms by the denominator


F*7F+4*7F-8=0

Wy multiply elements

7F^2+28F-8=0

a = 7; b = 28; c = -8;
Δ = b2-4ac
Δ = 282-4·7·(-8)
Δ = 1008
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:

$\sqrt{\Delta}=\sqrt{1008}=\sqrt{144*7}=\sqrt{144}*\sqrt{7}=12\sqrt{7}$
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(28)-12\sqrt{7}}{2*7}=\frac{-28-12\sqrt{7}}{14}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(28)+12\sqrt{7}}{2*7}=\frac{-28+12\sqrt{7}}{14}
$