2+1.25f=10-2/75f

Solution for 2+1.25f=10-2/75f equation:

2+1.25f=10-2/75f

We move all terms to the left:

2+1.25f-(10-2/75f)=0


Domain of the equation: 75f)!=0

f!=0/1

f!=0

f∈R


We add all the numbers together, and all the variables

1.25f-(-2/75f+10)+2=0

We get rid of parentheses

1.25f+2/75f-10+2=0

We multiply all the terms by the denominator


(1.25f)*75f-10*75f+2*75f+2=0

We add all the numbers together, and all the variables

(+1.25f)*75f-10*75f+2*75f+2=0

We multiply parentheses

75f^2-10*75f+2*75f+2=0

Wy multiply elements

75f^2-750f+150f+2=0

We add all the numbers together, and all the variables

75f^2-600f+2=0

a = 75; b = -600; c = +2;
Δ = b2-4ac
Δ = -6002-4·75·2
Δ = 359400
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:

$\sqrt{\Delta}=\sqrt{359400}=\sqrt{100*3594}=\sqrt{100}*\sqrt{3594}=10\sqrt{3594}$
$f_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-600)-10\sqrt{3594}}{2*75}=\frac{600-10\sqrt{3594}}{150}
$
$f_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-600)+10\sqrt{3594}}{2*75}=\frac{600+10\sqrt{3594}}{150}
$