9a(9+15a)=100

Solution for 9a(9+15a)=100 equation:

9a(9+15a)=100

We move all terms to the left:

9a(9+15a)-(100)=0

We add all the numbers together, and all the variables

9a(15a+9)-100=0

We multiply parentheses

135a^2+81a-100=0

a = 135; b = 81; c = -100;
Δ = b2-4ac
Δ = 812-4·135·(-100)
Δ = 60561
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{60561}=\sqrt{9*6729}=\sqrt{9}*\sqrt{6729}=3\sqrt{6729}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(81)-3\sqrt{6729}}{2*135}=\frac{-81-3\sqrt{6729}}{270}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(81)+3\sqrt{6729}}{2*135}=\frac{-81+3\sqrt{6729}}{270}
$