2a^2=75

Solution for 2a^2=75 equation:

2a^2=75

We move all terms to the left:

2a^2-(75)=0

a = 2; b = 0; c = -75;
Δ = b2-4ac
Δ = 02-4·2·(-75)
Δ = 600
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{600}=\sqrt{100*6}=\sqrt{100}*\sqrt{6}=10\sqrt{6}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-10\sqrt{6}}{2*2}=\frac{0-10\sqrt{6}}{4}
=-\frac{10\sqrt{6}}{4}
=-\frac{5\sqrt{6}}{2}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+10\sqrt{6}}{2*2}=\frac{0+10\sqrt{6}}{4}
=\frac{10\sqrt{6}}{4}
=\frac{5\sqrt{6}}{2}
$