8a^2+10=330

Solution for 8a^2+10=330 equation:

8a^2+10=330

We move all terms to the left:

8a^2+10-(330)=0

We add all the numbers together, and all the variables

8a^2-320=0

a = 8; b = 0; c = -320;
Δ = b2-4ac
Δ = 02-4·8·(-320)
Δ = 10240
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:

$\sqrt{\Delta}=\sqrt{10240}=\sqrt{1024*10}=\sqrt{1024}*\sqrt{10}=32\sqrt{10}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-32\sqrt{10}}{2*8}=\frac{0-32\sqrt{10}}{16}
=-\frac{32\sqrt{10}}{16}
=-2\sqrt{10}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+32\sqrt{10}}{2*8}=\frac{0+32\sqrt{10}}{16}
=\frac{32\sqrt{10}}{16}
=2\sqrt{10}
$