(4+3a)(5+5a)=20

Solution for (4+3a)(5+5a)=20 equation:

(4+3a)(5+5a)=20

We move all terms to the left:

(4+3a)(5+5a)-(20)=0

We add all the numbers together, and all the variables

(3a+4)(5a+5)-20=0

We multiply parentheses ..

(+15a^2+15a+20a+20)-20=0

We get rid of parentheses

15a^2+15a+20a+20-20=0

We add all the numbers together, and all the variables

15a^2+35a=0

a = 15; b = 35; c = 0;
Δ = b2-4ac
Δ = 352-4·15·0
Δ = 1225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1225}=35$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(35)-35}{2*15}=\frac{-70}{30}
=-2+1/3
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(35)+35}{2*15}=\frac{0}{30}
=0
$