(7a+6)(11a-5)=0

Solution for (7a+6)(11a-5)=0 equation:

(7a+6)(11a-5)=0

We multiply parentheses ..

(+77a^2-35a+66a-30)=0

We get rid of parentheses

77a^2-35a+66a-30=0

We add all the numbers together, and all the variables

77a^2+31a-30=0

a = 77; b = 31; c = -30;
Δ = b2-4ac
Δ = 312-4·77·(-30)
Δ = 10201
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{10201}=101$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(31)-101}{2*77}=\frac{-132}{154}
=-6/7
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(31)+101}{2*77}=\frac{70}{154}
=5/11
$