(4a+7)(a-5)=0

Solution for (4a+7)(a-5)=0 equation:

(4a+7)(a-5)=0

We multiply parentheses ..

(+4a^2-20a+7a-35)=0

We get rid of parentheses

4a^2-20a+7a-35=0

We add all the numbers together, and all the variables

4a^2-13a-35=0

a = 4; b = -13; c = -35;
Δ = b2-4ac
Δ = -132-4·4·(-35)
Δ = 729
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{729}=27$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-13)-27}{2*4}=\frac{-14}{8}
=-1+3/4
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-13)+27}{2*4}=\frac{40}{8}
=5
$