j2-7/3=25

Solution for j2-7/3=25 equation:

j2-7/3=25

We move all terms to the left:

j2-7/3-(25)=0

determiningTheFunctionDomain
j2-25-7/3=0

We add all the numbers together, and all the variables

j^2-25-7/3=0

We multiply all the terms by the denominator


j^2*3-7-25*3=0

We add all the numbers together, and all the variables

j^2*3-82=0

Wy multiply elements

3j^2-82=0

a = 3; b = 0; c = -82;
Δ = b2-4ac
Δ = 02-4·3·(-82)
Δ = 984
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$j_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$j_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{984}=\sqrt{4*246}=\sqrt{4}*\sqrt{246}=2\sqrt{246}$
$j_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{246}}{2*3}=\frac{0-2\sqrt{246}}{6}
=-\frac{2\sqrt{246}}{6}
=-\frac{\sqrt{246}}{3}
$
$j_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{246}}{2*3}=\frac{0+2\sqrt{246}}{6}
=\frac{2\sqrt{246}}{6}
=\frac{\sqrt{246}}{3}
$