2(3a-7)(5a-6)=90

Solution for 2(3a-7)(5a-6)=90 equation:

2(3a-7)(5a-6)=90

We move all terms to the left:

2(3a-7)(5a-6)-(90)=0

We multiply parentheses ..

2(+15a^2-18a-35a+42)-90=0

We multiply parentheses

30a^2-36a-70a+84-90=0

We add all the numbers together, and all the variables

30a^2-106a-6=0

a = 30; b = -106; c = -6;
Δ = b2-4ac
Δ = -1062-4·30·(-6)
Δ = 11956
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:

$\sqrt{\Delta}=\sqrt{11956}=\sqrt{196*61}=\sqrt{196}*\sqrt{61}=14\sqrt{61}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-106)-14\sqrt{61}}{2*30}=\frac{106-14\sqrt{61}}{60}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-106)+14\sqrt{61}}{2*30}=\frac{106+14\sqrt{61}}{60}
$