(3a-2)(a+5)=9a+5

Solution for (3a-2)(a+5)=9a+5 equation:

(3a-2)(a+5)=9a+5

We move all terms to the left:

(3a-2)(a+5)-(9a+5)=0

We get rid of parentheses

(3a-2)(a+5)-9a-5=0

We multiply parentheses ..

(+3a^2+15a-2a-10)-9a-5=0

We get rid of parentheses

3a^2+15a-2a-9a-10-5=0

We add all the numbers together, and all the variables

3a^2+4a-15=0

a = 3; b = 4; c = -15;
Δ = b2-4ac
Δ = 42-4·3·(-15)
Δ = 196
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{196}=14$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-14}{2*3}=\frac{-18}{6}
=-3
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+14}{2*3}=\frac{10}{6}
=1+2/3
$