62/3*f-5=5

Solution for 62/3*f-5=5 equation:

62/3*f-5=5

We move all terms to the left:

62/3*f-5-(5)=0


Domain of the equation: 3*f!=0

f!=0/1

f!=0

f∈R


We add all the numbers together, and all the variables

62/3*f-10=0

We multiply all the terms by the denominator


-10*3*f+62=0

Wy multiply elements

-30f*f+62=0

Wy multiply elements

-30f^2+62=0

a = -30; b = 0; c = +62;
Δ = b2-4ac
Δ = 02-4·(-30)·62
Δ = 7440
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:

$\sqrt{\Delta}=\sqrt{7440}=\sqrt{16*465}=\sqrt{16}*\sqrt{465}=4\sqrt{465}$
$f_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{465}}{2*-30}=\frac{0-4\sqrt{465}}{-60}
=-\frac{4\sqrt{465}}{-60}
=-\frac{\sqrt{465}}{-15}
$
$f_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{465}}{2*-30}=\frac{0+4\sqrt{465}}{-60}
=\frac{4\sqrt{465}}{-60}
=\frac{\sqrt{465}}{-15}
$