5=a^2-(a-3)

Solution for 5=a^2-(a-3) equation:

5=a^2-(a-3)

We move all terms to the left:

5-(a^2-(a-3))=0


We calculate terms in parentheses: -(a^2-(a-3)), so:

a^2-(a-3)

We get rid of parentheses

a^2-a+3

We add all the numbers together, and all the variables

a^2-1a+3

Back to the equation:

-(a^2-1a+3)


We get rid of parentheses

-a^2+1a-3+5=0

We add all the numbers together, and all the variables

-1a^2+a+2=0

a = -1; b = 1; c = +2;
Δ = b2-4ac
Δ = 12-4·(-1)·2
Δ = 9
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{9}=3$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-3}{2*-1}=\frac{-4}{-2}
=+2
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+3}{2*-1}=\frac{2}{-2}
=-1
$