24x^2+6x=16

Solution for 24x^2+6x=16 equation:

24x^2+6x=16

We move all terms to the left:

24x^2+6x-(16)=0

a = 24; b = 6; c = -16;
Δ = b2-4ac
Δ = 62-4·24·(-16)
Δ = 1572
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:

$\sqrt{\Delta}=\sqrt{1572}=\sqrt{4*393}=\sqrt{4}*\sqrt{393}=2\sqrt{393}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-2\sqrt{393}}{2*24}=\frac{-6-2\sqrt{393}}{48}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+2\sqrt{393}}{2*24}=\frac{-6+2\sqrt{393}}{48}
$