(4a+11)(3a-7)=0

Solution for (4a+11)(3a-7)=0 equation:

(4a+11)(3a-7)=0

We multiply parentheses ..

(+12a^2-28a+33a-77)=0

We get rid of parentheses

12a^2-28a+33a-77=0

We add all the numbers together, and all the variables

12a^2+5a-77=0

a = 12; b = 5; c = -77;
Δ = b2-4ac
Δ = 52-4·12·(-77)
Δ = 3721
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{3721}=61$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-61}{2*12}=\frac{-66}{24}
=-2+3/4
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+61}{2*12}=\frac{56}{24}
=2+1/3
$