5a^2+210=770

Solution for 5a^2+210=770 equation:

5a^2+210=770

We move all terms to the left:

5a^2+210-(770)=0

We add all the numbers together, and all the variables

5a^2-560=0

a = 5; b = 0; c = -560;
Δ = b2-4ac
Δ = 02-4·5·(-560)
Δ = 11200
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:

$\sqrt{\Delta}=\sqrt{11200}=\sqrt{1600*7}=\sqrt{1600}*\sqrt{7}=40\sqrt{7}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-40\sqrt{7}}{2*5}=\frac{0-40\sqrt{7}}{10}
=-\frac{40\sqrt{7}}{10}
=-4\sqrt{7}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+40\sqrt{7}}{2*5}=\frac{0+40\sqrt{7}}{10}
=\frac{40\sqrt{7}}{10}
=4\sqrt{7}
$