3(24x^2+2x-1)=0

Solution for 3(24x^2+2x-1)=0 equation:

3(24x^2+2x-1)=0

We multiply parentheses

72x^2+6x-3=0

a = 72; b = 6; c = -3;
Δ = b2-4ac
Δ = 62-4·72·(-3)
Δ = 900
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{900}=30$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-30}{2*72}=\frac{-36}{144}
=-1/4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+30}{2*72}=\frac{24}{144}
=1/6
$