-2+4/5f-3=f

Solution for -2+4/5f-3=f equation:

-2+4/5f-3=f

We move all terms to the left:

-2+4/5f-3-(f)=0


Domain of the equation: 5f!=0

f!=0/5

f!=0

f∈R


We add all the numbers together, and all the variables

-1f+4/5f-5=0

We multiply all the terms by the denominator


-1f*5f-5*5f+4=0

Wy multiply elements

-5f^2-25f+4=0

a = -5; b = -25; c = +4;
Δ = b2-4ac
Δ = -252-4·(-5)·4
Δ = 705
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{-(-25)-\sqrt{705}}{2*-5}=\frac{25-\sqrt{705}}{-10}
$
$f_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-25)+\sqrt{705}}{2*-5}=\frac{25+\sqrt{705}}{-10}
$