2x^2=1083

Solution for 2x^2=1083 equation:

2x^2=1083

We move all terms to the left:

2x^2-(1083)=0

a = 2; b = 0; c = -1083;
Δ = b2-4ac
Δ = 02-4·2·(-1083)
Δ = 8664
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:

$\sqrt{\Delta}=\sqrt{8664}=\sqrt{1444*6}=\sqrt{1444}*\sqrt{6}=38\sqrt{6}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-38\sqrt{6}}{2*2}=\frac{0-38\sqrt{6}}{4}
=-\frac{38\sqrt{6}}{4}
=-\frac{19\sqrt{6}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+38\sqrt{6}}{2*2}=\frac{0+38\sqrt{6}}{4}
=\frac{38\sqrt{6}}{4}
=\frac{19\sqrt{6}}{2}
$