3x2+2x-4=24

Solution for 3x2+2x-4=24 equation:

3x^2+2x-4=24

We move all terms to the left:

3x^2+2x-4-(24)=0

We add all the numbers together, and all the variables

3x^2+2x-28=0

a = 3; b = 2; c = -28;
Δ = b2-4ac
Δ = 22-4·3·(-28)
Δ = 340
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:

$\sqrt{\Delta}=\sqrt{340}=\sqrt{4*85}=\sqrt{4}*\sqrt{85}=2\sqrt{85}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-2\sqrt{85}}{2*3}=\frac{-2-2\sqrt{85}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2\sqrt{85}}{2*3}=\frac{-2+2\sqrt{85}}{6}
$