-10a^2+15=19a

Solution for -10a^2+15=19a equation:

-10a^2+15=19a

We move all terms to the left:

-10a^2+15-(19a)=0

a = -10; b = -19; c = +15;
Δ = b2-4ac
Δ = -192-4·(-10)·15
Δ = 961
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{961}=31$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-19)-31}{2*-10}=\frac{-12}{-20}
=3/5
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-19)+31}{2*-10}=\frac{50}{-20}
=-2+1/2
$