15-9a^2=-1885

Solution for 15-9a^2=-1885 equation:

15-9a^2=-1885

We move all terms to the left:

15-9a^2-(-1885)=0

We add all the numbers together, and all the variables

-9a^2+1900=0

a = -9; b = 0; c = +1900;
Δ = b2-4ac
Δ = 02-4·(-9)·1900
Δ = 68400
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:

$\sqrt{\Delta}=\sqrt{68400}=\sqrt{3600*19}=\sqrt{3600}*\sqrt{19}=60\sqrt{19}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-60\sqrt{19}}{2*-9}=\frac{0-60\sqrt{19}}{-18}
=-\frac{60\sqrt{19}}{-18}
=-\frac{10\sqrt{19}}{-3}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+60\sqrt{19}}{2*-9}=\frac{0+60\sqrt{19}}{-18}
=\frac{60\sqrt{19}}{-18}
=\frac{10\sqrt{19}}{-3}
$