F(x)=350+1/2x

Solution for F(x)=350+1/2x equation:

(F)=350+1/2F

We move all terms to the left:

(F)-(350+1/2F)=0


Domain of the equation: 2F)!=0

F!=0/1

F!=0

F∈R


We add all the numbers together, and all the variables

F-(1/2F+350)=0

We get rid of parentheses

F-1/2F-350=0

We multiply all the terms by the denominator


F*2F-350*2F-1=0

Wy multiply elements

2F^2-700F-1=0

a = 2; b = -700; c = -1;
Δ = b2-4ac
Δ = -7002-4·2·(-1)
Δ = 490008
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:

$\sqrt{\Delta}=\sqrt{490008}=\sqrt{4*122502}=\sqrt{4}*\sqrt{122502}=2\sqrt{122502}$
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-700)-2\sqrt{122502}}{2*2}=\frac{700-2\sqrt{122502}}{4}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-700)+2\sqrt{122502}}{2*2}=\frac{700+2\sqrt{122502}}{4}
$