10a^2+2=242

Solution for 10a^2+2=242 equation:

10a^2+2=242

We move all terms to the left:

10a^2+2-(242)=0

We add all the numbers together, and all the variables

10a^2-240=0

a = 10; b = 0; c = -240;
Δ = b2-4ac
Δ = 02-4·10·(-240)
Δ = 9600
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{9600}=\sqrt{1600*6}=\sqrt{1600}*\sqrt{6}=40\sqrt{6}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-40\sqrt{6}}{2*10}=\frac{0-40\sqrt{6}}{20}
=-\frac{40\sqrt{6}}{20}
=-2\sqrt{6}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+40\sqrt{6}}{2*10}=\frac{0+40\sqrt{6}}{20}
=\frac{40\sqrt{6}}{20}
=2\sqrt{6}
$