12a^2-5a-15=5a^2

Solution for 12a^2-5a-15=5a^2 equation:

12a^2-5a-15=5a^2

We move all terms to the left:

12a^2-5a-15-(5a^2)=0

determiningTheFunctionDomain
12a^2-5a^2-5a-15=0

We add all the numbers together, and all the variables

7a^2-5a-15=0

a = 7; b = -5; c = -15;
Δ = b2-4ac
Δ = -52-4·7·(-15)
Δ = 445
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-\sqrt{445}}{2*7}=\frac{5-\sqrt{445}}{14}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+\sqrt{445}}{2*7}=\frac{5+\sqrt{445}}{14}
$