(2a+7)(6a-8)=0

Solution for (2a+7)(6a-8)=0 equation:

(2a+7)(6a-8)=0

We multiply parentheses ..

(+12a^2-16a+42a-56)=0

We get rid of parentheses

12a^2-16a+42a-56=0

We add all the numbers together, and all the variables

12a^2+26a-56=0

a = 12; b = 26; c = -56;
Δ = b2-4ac
Δ = 262-4·12·(-56)
Δ = 3364
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{3364}=58$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(26)-58}{2*12}=\frac{-84}{24}
=-3+1/2
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(26)+58}{2*12}=\frac{32}{24}
=1+1/3
$