(a-5)2=a2-275

Solution for (a-5)2=a2-275 equation:

(a-5)2=a2-275

We move all terms to the left:

(a-5)2-(a2-275)=0

We add all the numbers together, and all the variables

-(+a^2-275)+(a-5)2=0

We multiply parentheses

-(+a^2-275)+2a-10=0

We get rid of parentheses

-a^2+2a+275-10=0

We add all the numbers together, and all the variables

-1a^2+2a+265=0

a = -1; b = 2; c = +265;
Δ = b2-4ac
Δ = 22-4·(-1)·265
Δ = 1064
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:

$\sqrt{\Delta}=\sqrt{1064}=\sqrt{4*266}=\sqrt{4}*\sqrt{266}=2\sqrt{266}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-2\sqrt{266}}{2*-1}=\frac{-2-2\sqrt{266}}{-2}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2\sqrt{266}}{2*-1}=\frac{-2+2\sqrt{266}}{-2}
$