6t(t+3)=42

Solution for 6t(t+3)=42 equation:

6t(t+3)=42

We move all terms to the left:

6t(t+3)-(42)=0

We multiply parentheses

6t^2+18t-42=0

a = 6; b = 18; c = -42;
Δ = b2-4ac
Δ = 182-4·6·(-42)
Δ = 1332
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:

$\sqrt{\Delta}=\sqrt{1332}=\sqrt{36*37}=\sqrt{36}*\sqrt{37}=6\sqrt{37}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(18)-6\sqrt{37}}{2*6}=\frac{-18-6\sqrt{37}}{12}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(18)+6\sqrt{37}}{2*6}=\frac{-18+6\sqrt{37}}{12}
$