19x^2=57

Solution for 19x^2=57 equation:

19x^2=57

We move all terms to the left:

19x^2-(57)=0

a = 19; b = 0; c = -57;
Δ = b2-4ac
Δ = 02-4·19·(-57)
Δ = 4332
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:

$\sqrt{\Delta}=\sqrt{4332}=\sqrt{1444*3}=\sqrt{1444}*\sqrt{3}=38\sqrt{3}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-38\sqrt{3}}{2*19}=\frac{0-38\sqrt{3}}{38}
=-\frac{38\sqrt{3}}{38}
=-\sqrt{3}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+38\sqrt{3}}{2*19}=\frac{0+38\sqrt{3}}{38}
=\frac{38\sqrt{3}}{38}
=\sqrt{3}
$