7a^2+10=227

Solution for 7a^2+10=227 equation:

7a^2+10=227

We move all terms to the left:

7a^2+10-(227)=0

We add all the numbers together, and all the variables

7a^2-217=0

a = 7; b = 0; c = -217;
Δ = b2-4ac
Δ = 02-4·7·(-217)
Δ = 6076
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:

$\sqrt{\Delta}=\sqrt{6076}=\sqrt{196*31}=\sqrt{196}*\sqrt{31}=14\sqrt{31}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-14\sqrt{31}}{2*7}=\frac{0-14\sqrt{31}}{14}
=-\frac{14\sqrt{31}}{14}
=-\sqrt{31}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+14\sqrt{31}}{2*7}=\frac{0+14\sqrt{31}}{14}
=\frac{14\sqrt{31}}{14}
=\sqrt{31}
$