F(x)=39/4x-17

Solution for F(x)=39/4x-17 equation:

(F)=39/4F-17

We move all terms to the left:

(F)-(39/4F-17)=0


Domain of the equation: 4F-17)!=0

F∈R


We get rid of parentheses

F-39/4F+17=0

We multiply all the terms by the denominator


F*4F+17*4F-39=0

Wy multiply elements

4F^2+68F-39=0

a = 4; b = 68; c = -39;
Δ = b2-4ac
Δ = 682-4·4·(-39)
Δ = 5248
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:

$\sqrt{\Delta}=\sqrt{5248}=\sqrt{64*82}=\sqrt{64}*\sqrt{82}=8\sqrt{82}$
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(68)-8\sqrt{82}}{2*4}=\frac{-68-8\sqrt{82}}{8}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(68)+8\sqrt{82}}{2*4}=\frac{-68+8\sqrt{82}}{8}
$