-2(2f-3)-1/2f=-3

Solution for -2(2f-3)-1/2f=-3 equation:

-2(2f-3)-1/2f=-3

We move all terms to the left:

-2(2f-3)-1/2f-(-3)=0


Domain of the equation: 2f!=0

f!=0/2

f!=0

f∈R


We add all the numbers together, and all the variables

-2(2f-3)-1/2f+3=0

We multiply parentheses

-4f-1/2f+6+3=0

We multiply all the terms by the denominator


-4f*2f+6*2f+3*2f-1=0

Wy multiply elements

-8f^2+12f+6f-1=0

We add all the numbers together, and all the variables

-8f^2+18f-1=0

a = -8; b = 18; c = -1;
Δ = b2-4ac
Δ = 182-4·(-8)·(-1)
Δ = 292
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:

$\sqrt{\Delta}=\sqrt{292}=\sqrt{4*73}=\sqrt{4}*\sqrt{73}=2\sqrt{73}$
$f_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(18)-2\sqrt{73}}{2*-8}=\frac{-18-2\sqrt{73}}{-16}
$
$f_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(18)+2\sqrt{73}}{2*-8}=\frac{-18+2\sqrt{73}}{-16}
$