t(-t+144)=224

Solution for t(-t+144)=224 equation:

t(-t+144)=224

We move all terms to the left:

t(-t+144)-(224)=0

We add all the numbers together, and all the variables

t(-1t+144)-224=0

We multiply parentheses

-1t^2+144t-224=0

a = -1; b = 144; c = -224;
Δ = b2-4ac
Δ = 1442-4·(-1)·(-224)
Δ = 19840
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{19840}=\sqrt{64*310}=\sqrt{64}*\sqrt{310}=8\sqrt{310}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(144)-8\sqrt{310}}{2*-1}=\frac{-144-8\sqrt{310}}{-2}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(144)+8\sqrt{310}}{2*-1}=\frac{-144+8\sqrt{310}}{-2}
$