F(x)=1/2x-7

Solution for F(x)=1/2x-7 equation:

(F)=1/2F-7

We move all terms to the left:

(F)-(1/2F-7)=0


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

F∈R


We get rid of parentheses

F-1/2F+7=0

We multiply all the terms by the denominator


F*2F+7*2F-1=0

Wy multiply elements

2F^2+14F-1=0

a = 2; b = 14; c = -1;
Δ = b2-4ac
Δ = 142-4·2·(-1)
Δ = 204
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:

$\sqrt{\Delta}=\sqrt{204}=\sqrt{4*51}=\sqrt{4}*\sqrt{51}=2\sqrt{51}$
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(14)-2\sqrt{51}}{2*2}=\frac{-14-2\sqrt{51}}{4}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(14)+2\sqrt{51}}{2*2}=\frac{-14+2\sqrt{51}}{4}
$