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

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

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

We move all terms to the left:

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

We get rid of parentheses

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

We multiply parentheses ..

(+6a^2+4a-9a-6)-14a-14=0

We get rid of parentheses

6a^2+4a-9a-14a-6-14=0

We add all the numbers together, and all the variables

6a^2-19a-20=0

a = 6; b = -19; c = -20;
Δ = b2-4ac
Δ = -192-4·6·(-20)
Δ = 841
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{841}=29$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-19)-29}{2*6}=\frac{-10}{12}
=-5/6
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-19)+29}{2*6}=\frac{48}{12}
=4
$