-16x^2+30x=9

Solution for -16x^2+30x=9 equation:

-16x^2+30x=9

We move all terms to the left:

-16x^2+30x-(9)=0

a = -16; b = 30; c = -9;
Δ = b2-4ac
Δ = 302-4·(-16)·(-9)
Δ = 324
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{324}=18$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(30)-18}{2*-16}=\frac{-48}{-32}
=1+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(30)+18}{2*-16}=\frac{-12}{-32}
=3/8
$