F(x)=6/2x-3=6

Solution for F(x)=6/2x-3=6 equation:

(F)=6/2F-3=6

We move all terms to the left:

(F)-(6/2F-3)=0


Domain of the equation: 2F-3)!=0

F∈R


We get rid of parentheses

F-6/2F+3=0

We multiply all the terms by the denominator


F*2F+3*2F-6=0

Wy multiply elements

2F^2+6F-6=0

a = 2; b = 6; c = -6;
Δ = b2-4ac
Δ = 62-4·2·(-6)
Δ = 84
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:

$\sqrt{\Delta}=\sqrt{84}=\sqrt{4*21}=\sqrt{4}*\sqrt{21}=2\sqrt{21}$
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-2\sqrt{21}}{2*2}=\frac{-6-2\sqrt{21}}{4}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+2\sqrt{21}}{2*2}=\frac{-6+2\sqrt{21}}{4}
$