128x-16x^2=30

Solution for 128x-16x^2=30 equation:

128x-16x^2=30

We move all terms to the left:

128x-16x^2-(30)=0

a = -16; b = 128; c = -30;
Δ = b2-4ac
Δ = 1282-4·(-16)·(-30)
Δ = 14464
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:

$\sqrt{\Delta}=\sqrt{14464}=\sqrt{64*226}=\sqrt{64}*\sqrt{226}=8\sqrt{226}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(128)-8\sqrt{226}}{2*-16}=\frac{-128-8\sqrt{226}}{-32}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(128)+8\sqrt{226}}{2*-16}=\frac{-128+8\sqrt{226}}{-32}
$