J(x)=144-x2

Solution for J(x)=144-x2 equation:

(J)=144-J2

We move all terms to the left:

(J)-(144-J2)=0

We add all the numbers together, and all the variables

-(-1J^2+144)+J=0

We get rid of parentheses

1J^2+J-144=0

We add all the numbers together, and all the variables

J^2+J-144=0

a = 1; b = 1; c = -144;
Δ = b2-4ac
Δ = 12-4·1·(-144)
Δ = 577
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{-(1)-\sqrt{577}}{2*1}=\frac{-1-\sqrt{577}}{2}
$
$J_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+\sqrt{577}}{2*1}=\frac{-1+\sqrt{577}}{2}
$