(6a+42)(18a-12)=90

Solution for (6a+42)(18a-12)=90 equation:

(6a+42)(18a-12)=90

We move all terms to the left:

(6a+42)(18a-12)-(90)=0

We multiply parentheses ..

(+108a^2-72a+756a-504)-90=0

We get rid of parentheses

108a^2-72a+756a-504-90=0

We add all the numbers together, and all the variables

108a^2+684a-594=0

a = 108; b = 684; c = -594;
Δ = b2-4ac
Δ = 6842-4·108·(-594)
Δ = 724464
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{724464}=\sqrt{1296*559}=\sqrt{1296}*\sqrt{559}=36\sqrt{559}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(684)-36\sqrt{559}}{2*108}=\frac{-684-36\sqrt{559}}{216}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(684)+36\sqrt{559}}{2*108}=\frac{-684+36\sqrt{559}}{216}
$