227x^2=1816

Solution for 227x^2=1816 equation:

227x^2=1816

We move all terms to the left:

227x^2-(1816)=0

a = 227; b = 0; c = -1816;
Δ = b2-4ac
Δ = 02-4·227·(-1816)
Δ = 1648928
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:

$\sqrt{\Delta}=\sqrt{1648928}=\sqrt{824464*2}=\sqrt{824464}*\sqrt{2}=908\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-908\sqrt{2}}{2*227}=\frac{0-908\sqrt{2}}{454}
=-\frac{908\sqrt{2}}{454}
=-2\sqrt{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+908\sqrt{2}}{2*227}=\frac{0+908\sqrt{2}}{454}
=\frac{908\sqrt{2}}{454}
=2\sqrt{2}
$