1/4f+1.1=8.3-f

Solution for 1/4f+1.1=8.3-f equation:

1/4f+1.1=8.3-f

We move all terms to the left:

1/4f+1.1-(8.3-f)=0


Domain of the equation: 4f!=0

f!=0/4

f!=0

f∈R


We add all the numbers together, and all the variables

1/4f-(-1f+8.3)+1.1=0

We get rid of parentheses

1/4f+1f-8.3+1.1=0

We multiply all the terms by the denominator


1f*4f-(8.3)*4f+(1.1)*4f+1=0

We multiply parentheses

1f*4f-33.2f+4.4f+1=0

Wy multiply elements

4f^2-33.2f+4.4f+1=0

We add all the numbers together, and all the variables

4f^2-28.8f+1=0

a = 4; b = -28.8; c = +1;
Δ = b2-4ac
Δ = -28.82-4·4·1
Δ = 813.44
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$f_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$f_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$f_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-28.8)-\sqrt{813.44}}{2*4}=\frac{28.8-\sqrt{813.44}}{8}
$
$f_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-28.8)+\sqrt{813.44}}{2*4}=\frac{28.8+\sqrt{813.44}}{8}
$