-32*x^2-288*x+900=0

Solution for -32*x^2-288*x+900=0 equation:

-32x^2-288x+900=0

a = -32; b = -288; c = +900;
Δ = b2-4ac
Δ = -2882-4·(-32)·900
Δ = 198144
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:

$\sqrt{\Delta}=\sqrt{198144}=\sqrt{2304*86}=\sqrt{2304}*\sqrt{86}=48\sqrt{86}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-288)-48\sqrt{86}}{2*-32}=\frac{288-48\sqrt{86}}{-64}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-288)+48\sqrt{86}}{2*-32}=\frac{288+48\sqrt{86}}{-64}
$