a^2-7a=a+20

Solution for a^2-7a=a+20 equation:

a^2-7a=a+20

We move all terms to the left:

a^2-7a-(a+20)=0

We get rid of parentheses

a^2-7a-a-20=0

We add all the numbers together, and all the variables

a^2-8a-20=0

a = 1; b = -8; c = -20;
Δ = b2-4ac
Δ = -82-4·1·(-20)
Δ = 144
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{144}=12$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-12}{2*1}=\frac{-4}{2}
=-2
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+12}{2*1}=\frac{20}{2}
=10
$