144x-16x^2=200

Solution for 144x-16x^2=200 equation:

144x-16x^2=200

We move all terms to the left:

144x-16x^2-(200)=0

a = -16; b = 144; c = -200;
Δ = b2-4ac
Δ = 1442-4·(-16)·(-200)
Δ = 7936
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:

$\sqrt{\Delta}=\sqrt{7936}=\sqrt{256*31}=\sqrt{256}*\sqrt{31}=16\sqrt{31}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(144)-16\sqrt{31}}{2*-16}=\frac{-144-16\sqrt{31}}{-32}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(144)+16\sqrt{31}}{2*-16}=\frac{-144+16\sqrt{31}}{-32}
$