15x^2=9x^2+83

Solution for 15x^2=9x^2+83 equation:

15x^2=9x^2+83

We move all terms to the left:

15x^2-(9x^2+83)=0

We get rid of parentheses

15x^2-9x^2-83=0

We add all the numbers together, and all the variables

6x^2-83=0

a = 6; b = 0; c = -83;
Δ = b2-4ac
Δ = 02-4·6·(-83)
Δ = 1992
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{1992}=\sqrt{4*498}=\sqrt{4}*\sqrt{498}=2\sqrt{498}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{498}}{2*6}=\frac{0-2\sqrt{498}}{12}
=-\frac{2\sqrt{498}}{12}
=-\frac{\sqrt{498}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{498}}{2*6}=\frac{0+2\sqrt{498}}{12}
=\frac{2\sqrt{498}}{12}
=\frac{\sqrt{498}}{6}
$