a^2+15=2a^2-16a

Solution for a^2+15=2a^2-16a equation:

a^2+15=2a^2-16a

We move all terms to the left:

a^2+15-(2a^2-16a)=0

We get rid of parentheses

a^2-2a^2+16a+15=0

We add all the numbers together, and all the variables

-1a^2+16a+15=0

a = -1; b = 16; c = +15;
Δ = b2-4ac
Δ = 162-4·(-1)·15
Δ = 316
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:

$\sqrt{\Delta}=\sqrt{316}=\sqrt{4*79}=\sqrt{4}*\sqrt{79}=2\sqrt{79}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(16)-2\sqrt{79}}{2*-1}=\frac{-16-2\sqrt{79}}{-2}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(16)+2\sqrt{79}}{2*-1}=\frac{-16+2\sqrt{79}}{-2}
$