F(x)=21/15x-33

Solution for F(x)=21/15x-33 equation:

(F)=21/15F-33

We move all terms to the left:

(F)-(21/15F-33)=0


Domain of the equation: 15F-33)!=0

F∈R


We get rid of parentheses

F-21/15F+33=0

We multiply all the terms by the denominator


F*15F+33*15F-21=0

Wy multiply elements

15F^2+495F-21=0

a = 15; b = 495; c = -21;
Δ = b2-4ac
Δ = 4952-4·15·(-21)
Δ = 246285
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:

$\sqrt{\Delta}=\sqrt{246285}=\sqrt{9*27365}=\sqrt{9}*\sqrt{27365}=3\sqrt{27365}$
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(495)-3\sqrt{27365}}{2*15}=\frac{-495-3\sqrt{27365}}{30}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(495)+3\sqrt{27365}}{2*15}=\frac{-495+3\sqrt{27365}}{30}
$