F(x)=-1/25x+15

Solution for F(x)=-1/25x+15 equation:

(F)=-1/25F+15

We move all terms to the left:

(F)-(-1/25F+15)=0


Domain of the equation: 25F+15)!=0

F∈R


We get rid of parentheses

F+1/25F-15=0

We multiply all the terms by the denominator


F*25F-15*25F+1=0

Wy multiply elements

25F^2-375F+1=0

a = 25; b = -375; c = +1;
Δ = b2-4ac
Δ = -3752-4·25·1
Δ = 140525
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:

$\sqrt{\Delta}=\sqrt{140525}=\sqrt{25*5621}=\sqrt{25}*\sqrt{5621}=5\sqrt{5621}$
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-375)-5\sqrt{5621}}{2*25}=\frac{375-5\sqrt{5621}}{50}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-375)+5\sqrt{5621}}{2*25}=\frac{375+5\sqrt{5621}}{50}
$