2.25f-12=1/4f-4

Solution for 2.25f-12=1/4f-4 equation:

2.25f-12=1/4f-4

We move all terms to the left:

2.25f-12-(1/4f-4)=0


Domain of the equation: 4f-4)!=0

f∈R


We get rid of parentheses

2.25f-1/4f+4-12=0

We multiply all the terms by the denominator


(2.25f)*4f+4*4f-12*4f-1=0

We add all the numbers together, and all the variables

(+2.25f)*4f+4*4f-12*4f-1=0

We multiply parentheses

8f^2+4*4f-12*4f-1=0

Wy multiply elements

8f^2+16f-48f-1=0

We add all the numbers together, and all the variables

8f^2-32f-1=0

a = 8; b = -32; c = -1;
Δ = b2-4ac
Δ = -322-4·8·(-1)
Δ = 1056
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:

$\sqrt{\Delta}=\sqrt{1056}=\sqrt{16*66}=\sqrt{16}*\sqrt{66}=4\sqrt{66}$
$f_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-32)-4\sqrt{66}}{2*8}=\frac{32-4\sqrt{66}}{16}
$
$f_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-32)+4\sqrt{66}}{2*8}=\frac{32+4\sqrt{66}}{16}
$