(6a+42)(18a-12)=a

Solution for (6a+42)(18a-12)=a equation:

(6a+42)(18a-12)=a

We move all terms to the left:

(6a+42)(18a-12)-(a)=0

We add all the numbers together, and all the variables

-1a+(6a+42)(18a-12)=0

We multiply parentheses ..

(+108a^2-72a+756a-504)-1a=0

We get rid of parentheses

108a^2-72a+756a-1a-504=0

We add all the numbers together, and all the variables

108a^2+683a-504=0

a = 108; b = 683; c = -504;
Δ = b2-4ac
Δ = 6832-4·108·(-504)
Δ = 684217
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{-(683)-\sqrt{684217}}{2*108}=\frac{-683-\sqrt{684217}}{216}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(683)+\sqrt{684217}}{2*108}=\frac{-683+\sqrt{684217}}{216}
$