2(a-5)=a^2-13

Solution for 2(a-5)=a^2-13 equation:

2(a-5)=a^2-13

We move all terms to the left:

2(a-5)-(a^2-13)=0

We multiply parentheses

2a-(a^2-13)-10=0

We get rid of parentheses

-a^2+2a+13-10=0

We add all the numbers together, and all the variables

-1a^2+2a+3=0

a = -1; b = 2; c = +3;
Δ = b2-4ac
Δ = 22-4·(-1)·3
Δ = 16
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{16}=4$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-4}{2*-1}=\frac{-6}{-2}
=+3
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+4}{2*-1}=\frac{2}{-2}
=-1
$