F(x)=7/2x-7

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

(F)=7/2F-7

We move all terms to the left:

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


Domain of the equation: 2F-7)!=0

F∈R


We get rid of parentheses

F-7/2F+7=0

We multiply all the terms by the denominator


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

Wy multiply elements

2F^2+14F-7=0

a = 2; b = 14; c = -7;
Δ = b2-4ac
Δ = 142-4·2·(-7)
Δ = 252
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:

$\sqrt{\Delta}=\sqrt{252}=\sqrt{36*7}=\sqrt{36}*\sqrt{7}=6\sqrt{7}$
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(14)-6\sqrt{7}}{2*2}=\frac{-14-6\sqrt{7}}{4}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(14)+6\sqrt{7}}{2*2}=\frac{-14+6\sqrt{7}}{4}
$