t(t+-24)=-100

Solution for t(t+-24)=-100 equation:

t(t+-24)=-100

We move all terms to the left:

t(t+-24)-(-100)=0

We add all the numbers together, and all the variables

t(t-24)-(-100)=0

We add all the numbers together, and all the variables

t(t-24)+100=0

We multiply parentheses

t^2-24t+100=0

a = 1; b = -24; c = +100;
Δ = b2-4ac
Δ = -242-4·1·100
Δ = 176
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:

$\sqrt{\Delta}=\sqrt{176}=\sqrt{16*11}=\sqrt{16}*\sqrt{11}=4\sqrt{11}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-24)-4\sqrt{11}}{2*1}=\frac{24-4\sqrt{11}}{2}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-24)+4\sqrt{11}}{2*1}=\frac{24+4\sqrt{11}}{2}
$