(6a+7)(15a+9)=0

Solution for (6a+7)(15a+9)=0 equation:

(6a+7)(15a+9)=0

We multiply parentheses ..

(+90a^2+54a+105a+63)=0

We get rid of parentheses

90a^2+54a+105a+63=0

We add all the numbers together, and all the variables

90a^2+159a+63=0

a = 90; b = 159; c = +63;
Δ = b2-4ac
Δ = 1592-4·90·63
Δ = 2601
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2601}=51$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(159)-51}{2*90}=\frac{-210}{180}
=-1+1/6
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(159)+51}{2*90}=\frac{-108}{180}
=-3/5
$