2x2-100=-3x2+96

Solution for 2x2-100=-3x2+96 equation:

2x^2-100=-3x^2+96

We move all terms to the left:

2x^2-100-(-3x^2+96)=0

We get rid of parentheses

2x^2+3x^2-96-100=0

We add all the numbers together, and all the variables

5x^2-196=0

a = 5; b = 0; c = -196;
Δ = b2-4ac
Δ = 02-4·5·(-196)
Δ = 3920
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:

$\sqrt{\Delta}=\sqrt{3920}=\sqrt{784*5}=\sqrt{784}*\sqrt{5}=28\sqrt{5}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-28\sqrt{5}}{2*5}=\frac{0-28\sqrt{5}}{10}
=-\frac{28\sqrt{5}}{10}
=-\frac{14\sqrt{5}}{5}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+28\sqrt{5}}{2*5}=\frac{0+28\sqrt{5}}{10}
=\frac{28\sqrt{5}}{10}
=\frac{14\sqrt{5}}{5}
$