F(x)=-2/3(x)-5

Solution for F(x)=-2/3(x)-5 equation:

(F)=-2/3(F)-5

We move all terms to the left:

(F)-(-2/3(F)-5)=0


Domain of the equation: 3F-5)!=0

F∈R


We get rid of parentheses

F+2/3F+5=0

We multiply all the terms by the denominator


F*3F+5*3F+2=0

Wy multiply elements

3F^2+15F+2=0

a = 3; b = 15; c = +2;
Δ = b2-4ac
Δ = 152-4·3·2
Δ = 201
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{-(15)-\sqrt{201}}{2*3}=\frac{-15-\sqrt{201}}{6}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(15)+\sqrt{201}}{2*3}=\frac{-15+\sqrt{201}}{6}
$