F(x)=45/11x-28

Solution for F(x)=45/11x-28 equation:

(F)=45/11F-28

We move all terms to the left:

(F)-(45/11F-28)=0


Domain of the equation: 11F-28)!=0

F∈R


We get rid of parentheses

F-45/11F+28=0

We multiply all the terms by the denominator


F*11F+28*11F-45=0

Wy multiply elements

11F^2+308F-45=0

a = 11; b = 308; c = -45;
Δ = b2-4ac
Δ = 3082-4·11·(-45)
Δ = 96844
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:

$\sqrt{\Delta}=\sqrt{96844}=\sqrt{4*24211}=\sqrt{4}*\sqrt{24211}=2\sqrt{24211}$
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(308)-2\sqrt{24211}}{2*11}=\frac{-308-2\sqrt{24211}}{22}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(308)+2\sqrt{24211}}{2*11}=\frac{-308+2\sqrt{24211}}{22}
$