2(5a+7)3a=-14

Solution for 2(5a+7)3a=-14 equation:

2(5a+7)3a=-14

We move all terms to the left:

2(5a+7)3a-(-14)=0

We add all the numbers together, and all the variables

2(5a+7)3a+14=0

We multiply parentheses

30a^2+42a+14=0

a = 30; b = 42; c = +14;
Δ = b2-4ac
Δ = 422-4·30·14
Δ = 84
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:

$\sqrt{\Delta}=\sqrt{84}=\sqrt{4*21}=\sqrt{4}*\sqrt{21}=2\sqrt{21}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(42)-2\sqrt{21}}{2*30}=\frac{-42-2\sqrt{21}}{60}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(42)+2\sqrt{21}}{2*30}=\frac{-42+2\sqrt{21}}{60}
$