10a-a^2=15

Solution for 10a-a^2=15 equation:

10a-a^2=15

We move all terms to the left:

10a-a^2-(15)=0

We add all the numbers together, and all the variables

-1a^2+10a-15=0

a = -1; b = 10; c = -15;
Δ = b2-4ac
Δ = 102-4·(-1)·(-15)
Δ = 40
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:

$\sqrt{\Delta}=\sqrt{40}=\sqrt{4*10}=\sqrt{4}*\sqrt{10}=2\sqrt{10}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-2\sqrt{10}}{2*-1}=\frac{-10-2\sqrt{10}}{-2}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+2\sqrt{10}}{2*-1}=\frac{-10+2\sqrt{10}}{-2}
$