15a=(a^2-3a+12)

Solution for 15a=(a^2-3a+12) equation:

15a=(a^2-3a+12)

We move all terms to the left:

15a-((a^2-3a+12))=0


We calculate terms in parentheses: -((a^2-3a+12)), so:

(a^2-3a+12)

We get rid of parentheses

a^2-3a+12

Back to the equation:

-(a^2-3a+12)


We get rid of parentheses

-a^2+15a+3a-12=0

We add all the numbers together, and all the variables

-1a^2+18a-12=0

a = -1; b = 18; c = -12;
Δ = b2-4ac
Δ = 182-4·(-1)·(-12)
Δ = 276
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:

$\sqrt{\Delta}=\sqrt{276}=\sqrt{4*69}=\sqrt{4}*\sqrt{69}=2\sqrt{69}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(18)-2\sqrt{69}}{2*-1}=\frac{-18-2\sqrt{69}}{-2}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(18)+2\sqrt{69}}{2*-1}=\frac{-18+2\sqrt{69}}{-2}
$