-5a^2+7=a^2-593

Solution for -5a^2+7=a^2-593 equation:

-5a^2+7=a^2-593

We move all terms to the left:

-5a^2+7-(a^2-593)=0

We get rid of parentheses

-5a^2-a^2+593+7=0

We add all the numbers together, and all the variables

-6a^2+600=0

a = -6; b = 0; c = +600;
Δ = b2-4ac
Δ = 02-4·(-6)·600
Δ = 14400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{14400}=120$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-120}{2*-6}=\frac{-120}{-12}
=+10
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+120}{2*-6}=\frac{120}{-12}
=-10
$