9a^2+8=278

Solution for 9a^2+8=278 equation:

9a^2+8=278

We move all terms to the left:

9a^2+8-(278)=0

We add all the numbers together, and all the variables

9a^2-270=0

a = 9; b = 0; c = -270;
Δ = b2-4ac
Δ = 02-4·9·(-270)
Δ = 9720
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:

$\sqrt{\Delta}=\sqrt{9720}=\sqrt{324*30}=\sqrt{324}*\sqrt{30}=18\sqrt{30}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-18\sqrt{30}}{2*9}=\frac{0-18\sqrt{30}}{18}
=-\frac{18\sqrt{30}}{18}
=-\sqrt{30}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+18\sqrt{30}}{2*9}=\frac{0+18\sqrt{30}}{18}
=\frac{18\sqrt{30}}{18}
=\sqrt{30}
$