10x^2+1=61

Solution for 10x^2+1=61 equation:

10x^2+1=61

We move all terms to the left:

10x^2+1-(61)=0

We add all the numbers together, and all the variables

10x^2-60=0

a = 10; b = 0; c = -60;
Δ = b2-4ac
Δ = 02-4·10·(-60)
Δ = 2400
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:

$\sqrt{\Delta}=\sqrt{2400}=\sqrt{400*6}=\sqrt{400}*\sqrt{6}=20\sqrt{6}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-20\sqrt{6}}{2*10}=\frac{0-20\sqrt{6}}{20}
=-\frac{20\sqrt{6}}{20}
=-\sqrt{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+20\sqrt{6}}{2*10}=\frac{0+20\sqrt{6}}{20}
=\frac{20\sqrt{6}}{20}
=\sqrt{6}
$