12x^2+16x^2=24

Solution for 12x^2+16x^2=24 equation:

12x^2+16x^2=24

We move all terms to the left:

12x^2+16x^2-(24)=0

We add all the numbers together, and all the variables

28x^2-24=0

a = 28; b = 0; c = -24;
Δ = b2-4ac
Δ = 02-4·28·(-24)
Δ = 2688
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:

$\sqrt{\Delta}=\sqrt{2688}=\sqrt{64*42}=\sqrt{64}*\sqrt{42}=8\sqrt{42}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-8\sqrt{42}}{2*28}=\frac{0-8\sqrt{42}}{56}
=-\frac{8\sqrt{42}}{56}
=-\frac{\sqrt{42}}{7}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+8\sqrt{42}}{2*28}=\frac{0+8\sqrt{42}}{56}
=\frac{8\sqrt{42}}{56}
=\frac{\sqrt{42}}{7}
$