6a2-14a=12

Solution for 6a2-14a=12 equation:

6a^2-14a=12

We move all terms to the left:

6a^2-14a-(12)=0

a = 6; b = -14; c = -12;
Δ = b2-4ac
Δ = -142-4·6·(-12)
Δ = 484
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{484}=22$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-14)-22}{2*6}=\frac{-8}{12}
=-2/3
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-14)+22}{2*6}=\frac{36}{12}
=3
$