4(3a^2+2a-7)=0

Solution for 4(3a^2+2a-7)=0 equation:

4(3a^2+2a-7)=0

We multiply parentheses

12a^2+8a-28=0

a = 12; b = 8; c = -28;
Δ = b2-4ac
Δ = 82-4·12·(-28)
Δ = 1408
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:

$\sqrt{\Delta}=\sqrt{1408}=\sqrt{64*22}=\sqrt{64}*\sqrt{22}=8\sqrt{22}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-8\sqrt{22}}{2*12}=\frac{-8-8\sqrt{22}}{24}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+8\sqrt{22}}{2*12}=\frac{-8+8\sqrt{22}}{24}
$