J(x)=-1/3x+5

Solution for J(x)=-1/3x+5 equation:

(J)=-1/3J+5

We move all terms to the left:

(J)-(-1/3J+5)=0


Domain of the equation: 3J+5)!=0

J∈R


We get rid of parentheses

J+1/3J-5=0

We multiply all the terms by the denominator


J*3J-5*3J+1=0

Wy multiply elements

3J^2-15J+1=0

a = 3; b = -15; c = +1;
Δ = b2-4ac
Δ = -152-4·3·1
Δ = 213
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$J_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$J_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$J_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-15)-\sqrt{213}}{2*3}=\frac{15-\sqrt{213}}{6}
$
$J_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-15)+\sqrt{213}}{2*3}=\frac{15+\sqrt{213}}{6}
$