3t2=7t+6

Solution for 3t2=7t+6 equation:

3t^2=7t+6

We move all terms to the left:

3t^2-(7t+6)=0

We get rid of parentheses

3t^2-7t-6=0

a = 3; b = -7; c = -6;
Δ = b2-4ac
Δ = -72-4·3·(-6)
Δ = 121
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{121}=11$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-7)-11}{2*3}=\frac{-4}{6}
=-2/3
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+11}{2*3}=\frac{18}{6}
=3
$