3x^2+11-24x=0

Solution for 3x^2+11-24x=0 equation:

3x^2+11-24x=0

a = 3; b = -24; c = +11;
Δ = b2-4ac
Δ = -242-4·3·11
Δ = 444
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:

$\sqrt{\Delta}=\sqrt{444}=\sqrt{4*111}=\sqrt{4}*\sqrt{111}=2\sqrt{111}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-24)-2\sqrt{111}}{2*3}=\frac{24-2\sqrt{111}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-24)+2\sqrt{111}}{2*3}=\frac{24+2\sqrt{111}}{6}
$