10a^2+1=151

Solution for 10a^2+1=151 equation:

10a^2+1=151

We move all terms to the left:

10a^2+1-(151)=0

We add all the numbers together, and all the variables

10a^2-150=0

a = 10; b = 0; c = -150;
Δ = b2-4ac
Δ = 02-4·10·(-150)
Δ = 6000
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:

$\sqrt{\Delta}=\sqrt{6000}=\sqrt{400*15}=\sqrt{400}*\sqrt{15}=20\sqrt{15}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-20\sqrt{15}}{2*10}=\frac{0-20\sqrt{15}}{20}
=-\frac{20\sqrt{15}}{20}
=-\sqrt{15}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+20\sqrt{15}}{2*10}=\frac{0+20\sqrt{15}}{20}
=\frac{20\sqrt{15}}{20}
=\sqrt{15}
$