53x^2=2240

Solution for 53x^2=2240 equation:

53x^2=2240

We move all terms to the left:

53x^2-(2240)=0

a = 53; b = 0; c = -2240;
Δ = b2-4ac
Δ = 02-4·53·(-2240)
Δ = 474880
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:

$\sqrt{\Delta}=\sqrt{474880}=\sqrt{256*1855}=\sqrt{256}*\sqrt{1855}=16\sqrt{1855}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-16\sqrt{1855}}{2*53}=\frac{0-16\sqrt{1855}}{106}
=-\frac{16\sqrt{1855}}{106}
=-\frac{8\sqrt{1855}}{53}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+16\sqrt{1855}}{2*53}=\frac{0+16\sqrt{1855}}{106}
=\frac{16\sqrt{1855}}{106}
=\frac{8\sqrt{1855}}{53}
$