5a^2-7=78

Solution for 5a^2-7=78 equation:

5a^2-7=78

We move all terms to the left:

5a^2-7-(78)=0

We add all the numbers together, and all the variables

5a^2-85=0

a = 5; b = 0; c = -85;
Δ = b2-4ac
Δ = 02-4·5·(-85)
Δ = 1700
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:

$\sqrt{\Delta}=\sqrt{1700}=\sqrt{100*17}=\sqrt{100}*\sqrt{17}=10\sqrt{17}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-10\sqrt{17}}{2*5}=\frac{0-10\sqrt{17}}{10}
=-\frac{10\sqrt{17}}{10}
=-\sqrt{17}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+10\sqrt{17}}{2*5}=\frac{0+10\sqrt{17}}{10}
=\frac{10\sqrt{17}}{10}
=\sqrt{17}
$