288=-16x^2+144x

Solution for 288=-16x^2+144x equation:

288=-16x^2+144x

We move all terms to the left:

288-(-16x^2+144x)=0

We get rid of parentheses

16x^2-144x+288=0

a = 16; b = -144; c = +288;
Δ = b2-4ac
Δ = -1442-4·16·288
Δ = 2304
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2304}=48$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-144)-48}{2*16}=\frac{96}{32}
=3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-144)+48}{2*16}=\frac{192}{32}
=6
$