8x2-24=3x2-9

Solution for 8x2-24=3x2-9 equation:

8x^2-24=3x^2-9

We move all terms to the left:

8x^2-24-(3x^2-9)=0

We get rid of parentheses

8x^2-3x^2+9-24=0

We add all the numbers together, and all the variables

5x^2-15=0

a = 5; b = 0; c = -15;
Δ = b2-4ac
Δ = 02-4·5·(-15)
Δ = 300
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:

$\sqrt{\Delta}=\sqrt{300}=\sqrt{100*3}=\sqrt{100}*\sqrt{3}=10\sqrt{3}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-10\sqrt{3}}{2*5}=\frac{0-10\sqrt{3}}{10}
=-\frac{10\sqrt{3}}{10}
=-\sqrt{3}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+10\sqrt{3}}{2*5}=\frac{0+10\sqrt{3}}{10}
=\frac{10\sqrt{3}}{10}
=\sqrt{3}
$