F(x)=(5x-10/3)

Solution for F(x)=(5x-10/3) equation:

(F)=(5F-10/3)

We move all terms to the left:

(F)-((5F-10/3))=0

We add all the numbers together, and all the variables

F-((+5F-10/3))=0

We multiply all the terms by the denominator


F*3))-((+5F-10=0

We add all the numbers together, and all the variables

5F+F*3))-((-10=0

Wy multiply elements

3F^2+5F-10=0

a = 3; b = 5; c = -10;
Δ = b2-4ac
Δ = 52-4·3·(-10)
Δ = 145
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{-(5)-\sqrt{145}}{2*3}=\frac{-5-\sqrt{145}}{6}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+\sqrt{145}}{2*3}=\frac{-5+\sqrt{145}}{6}
$