F(x)=4x-3/2x+1

Solution for F(x)=4x-3/2x+1 equation:

(F)=4F-3/2F+1

We move all terms to the left:

(F)-(4F-3/2F+1)=0


Domain of the equation: 2F+1)!=0

F∈R


We get rid of parentheses

F-4F+3/2F-1=0

We multiply all the terms by the denominator


F*2F-4F*2F-1*2F+3=0

Wy multiply elements

2F^2-8F^2-2F+3=0

We add all the numbers together, and all the variables

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

a = -6; b = -2; c = +3;
Δ = b2-4ac
Δ = -22-4·(-6)·3
Δ = 76
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:

$\sqrt{\Delta}=\sqrt{76}=\sqrt{4*19}=\sqrt{4}*\sqrt{19}=2\sqrt{19}$
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-2\sqrt{19}}{2*-6}=\frac{2-2\sqrt{19}}{-12}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+2\sqrt{19}}{2*-6}=\frac{2+2\sqrt{19}}{-12}
$