10x^2=410

Solution for 10x^2=410 equation:

10x^2=410

We move all terms to the left:

10x^2-(410)=0

a = 10; b = 0; c = -410;
Δ = b2-4ac
Δ = 02-4·10·(-410)
Δ = 16400
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:

$\sqrt{\Delta}=\sqrt{16400}=\sqrt{400*41}=\sqrt{400}*\sqrt{41}=20\sqrt{41}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-20\sqrt{41}}{2*10}=\frac{0-20\sqrt{41}}{20}
=-\frac{20\sqrt{41}}{20}
=-\sqrt{41}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+20\sqrt{41}}{2*10}=\frac{0+20\sqrt{41}}{20}
=\frac{20\sqrt{41}}{20}
=\sqrt{41}
$