(3t+3)(3t+5)=75

Solution for (3t+3)(3t+5)=75 equation:

(3t+3)(3t+5)=75

We move all terms to the left:

(3t+3)(3t+5)-(75)=0

We multiply parentheses ..

(+9t^2+15t+9t+15)-75=0

We get rid of parentheses

9t^2+15t+9t+15-75=0

We add all the numbers together, and all the variables

9t^2+24t-60=0

a = 9; b = 24; c = -60;
Δ = b2-4ac
Δ = 242-4·9·(-60)
Δ = 2736
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:

$\sqrt{\Delta}=\sqrt{2736}=\sqrt{144*19}=\sqrt{144}*\sqrt{19}=12\sqrt{19}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(24)-12\sqrt{19}}{2*9}=\frac{-24-12\sqrt{19}}{18}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(24)+12\sqrt{19}}{2*9}=\frac{-24+12\sqrt{19}}{18}
$