(-a+1)(5a+6)=5a^2

Solution for (-a+1)(5a+6)=5a^2 equation:

(-a+1)(5a+6)=5a^2

We move all terms to the left:

(-a+1)(5a+6)-(5a^2)=0

determiningTheFunctionDomain
-5a^2+(-a+1)(5a+6)=0

We add all the numbers together, and all the variables

-5a^2+(-1a+1)(5a+6)=0

We multiply parentheses ..

-5a^2+(-5a^2-6a+5a+6)=0

We get rid of parentheses

-5a^2-5a^2-6a+5a+6=0

We add all the numbers together, and all the variables

-10a^2-1a+6=0

a = -10; b = -1; c = +6;
Δ = b2-4ac
Δ = -12-4·(-10)·6
Δ = 241
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-\sqrt{241}}{2*-10}=\frac{1-\sqrt{241}}{-20}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+\sqrt{241}}{2*-10}=\frac{1+\sqrt{241}}{-20}
$