9x^2-30x=16

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

9x^2-30x=16

We move all terms to the left:

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

a = 9; b = -30; c = -16;
Δ = b2-4ac
Δ = -302-4·9·(-16)
Δ = 1476
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{1476}=\sqrt{36*41}=\sqrt{36}*\sqrt{41}=6\sqrt{41}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-30)-6\sqrt{41}}{2*9}=\frac{30-6\sqrt{41}}{18}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-30)+6\sqrt{41}}{2*9}=\frac{30+6\sqrt{41}}{18}
$