-6a(a+5)+5a=12+6a

Solution for -6a(a+5)+5a=12+6a equation:

-6a(a+5)+5a=12+6a

We move all terms to the left:

-6a(a+5)+5a-(12+6a)=0

We add all the numbers together, and all the variables

-6a(a+5)+5a-(6a+12)=0

We add all the numbers together, and all the variables

5a-6a(a+5)-(6a+12)=0

We multiply parentheses

-6a^2+5a-30a-(6a+12)=0

We get rid of parentheses

-6a^2+5a-30a-6a-12=0

We add all the numbers together, and all the variables

-6a^2-31a-12=0

a = -6; b = -31; c = -12;
Δ = b2-4ac
Δ = -312-4·(-6)·(-12)
Δ = 673
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{-(-31)-\sqrt{673}}{2*-6}=\frac{31-\sqrt{673}}{-12}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-31)+\sqrt{673}}{2*-6}=\frac{31+\sqrt{673}}{-12}
$