2(5x^2x-3)=0

Solution for 2(5x^2x-3)=0 equation:

2(5x^2x-3)=0

We multiply parentheses

10x^2-6=0

a = 10; b = 0; c = -6;
Δ = b2-4ac
Δ = 02-4·10·(-6)
Δ = 240
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:

$\sqrt{\Delta}=\sqrt{240}=\sqrt{16*15}=\sqrt{16}*\sqrt{15}=4\sqrt{15}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{15}}{2*10}=\frac{0-4\sqrt{15}}{20}
=-\frac{4\sqrt{15}}{20}
=-\frac{\sqrt{15}}{5}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{15}}{2*10}=\frac{0+4\sqrt{15}}{20}
=\frac{4\sqrt{15}}{20}
=\frac{\sqrt{15}}{5}
$