6x^2=2.5

Solution for 6x^2=2.5 equation:

6x^2=2.5

We move all terms to the left:

6x^2-(2.5)=0

We add all the numbers together, and all the variables

6x^2-2.5=0

a = 6; b = 0; c = -2.5;
Δ = b2-4ac
Δ = 02-4·6·(-2.5)
Δ = 60
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:

$\sqrt{\Delta}=\sqrt{60}=\sqrt{4*15}=\sqrt{4}*\sqrt{15}=2\sqrt{15}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{15}}{2*6}=\frac{0-2\sqrt{15}}{12}
=-\frac{2\sqrt{15}}{12}
=-\frac{\sqrt{15}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{15}}{2*6}=\frac{0+2\sqrt{15}}{12}
=\frac{2\sqrt{15}}{12}
=\frac{\sqrt{15}}{6}
$