F(x)=-1/3x+10

Solution for F(x)=-1/3x+10 equation:

(F)=-1/3F+10

We move all terms to the left:

(F)-(-1/3F+10)=0


Domain of the equation: 3F+10)!=0

F∈R


We get rid of parentheses

F+1/3F-10=0

We multiply all the terms by the denominator


F*3F-10*3F+1=0

Wy multiply elements

3F^2-30F+1=0

a = 3; b = -30; c = +1;
Δ = b2-4ac
Δ = -302-4·3·1
Δ = 888
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:

$\sqrt{\Delta}=\sqrt{888}=\sqrt{4*222}=\sqrt{4}*\sqrt{222}=2\sqrt{222}$
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-30)-2\sqrt{222}}{2*3}=\frac{30-2\sqrt{222}}{6}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-30)+2\sqrt{222}}{2*3}=\frac{30+2\sqrt{222}}{6}
$