20x^2-x^2-96=0

Solution for 20x^2-x^2-96=0 equation:

20x^2-x^2-96=0

We add all the numbers together, and all the variables

19x^2-96=0

a = 19; b = 0; c = -96;
Δ = b2-4ac
Δ = 02-4·19·(-96)
Δ = 7296
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:

$\sqrt{\Delta}=\sqrt{7296}=\sqrt{64*114}=\sqrt{64}*\sqrt{114}=8\sqrt{114}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-8\sqrt{114}}{2*19}=\frac{0-8\sqrt{114}}{38}
=-\frac{8\sqrt{114}}{38}
=-\frac{4\sqrt{114}}{19}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+8\sqrt{114}}{2*19}=\frac{0+8\sqrt{114}}{38}
=\frac{8\sqrt{114}}{38}
=\frac{4\sqrt{114}}{19}
$