(2a+7)(7a-4)=0

Solution for (2a+7)(7a-4)=0 equation:

(2a+7)(7a-4)=0

We multiply parentheses ..

(+14a^2-8a+49a-28)=0

We get rid of parentheses

14a^2-8a+49a-28=0

We add all the numbers together, and all the variables

14a^2+41a-28=0

a = 14; b = 41; c = -28;
Δ = b2-4ac
Δ = 412-4·14·(-28)
Δ = 3249
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{3249}=57$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(41)-57}{2*14}=\frac{-98}{28}
=-3+1/2
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(41)+57}{2*14}=\frac{16}{28}
=4/7
$