(2a+1)(3a+1)=70

Solution for (2a+1)(3a+1)=70 equation:

(2a+1)(3a+1)=70

We move all terms to the left:

(2a+1)(3a+1)-(70)=0

We multiply parentheses ..

(+6a^2+2a+3a+1)-70=0

We get rid of parentheses

6a^2+2a+3a+1-70=0

We add all the numbers together, and all the variables

6a^2+5a-69=0

a = 6; b = 5; c = -69;
Δ = b2-4ac
Δ = 52-4·6·(-69)
Δ = 1681
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1681}=41$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-41}{2*6}=\frac{-46}{12}
=-3+5/6
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+41}{2*6}=\frac{36}{12}
=3
$