4t^2=6t+6

Solution for 4t^2=6t+6 equation:

4t^2=6t+6

We move all terms to the left:

4t^2-(6t+6)=0

We get rid of parentheses

4t^2-6t-6=0

a = 4; b = -6; c = -6;
Δ = b2-4ac
Δ = -62-4·4·(-6)
Δ = 132
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:

$\sqrt{\Delta}=\sqrt{132}=\sqrt{4*33}=\sqrt{4}*\sqrt{33}=2\sqrt{33}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-2\sqrt{33}}{2*4}=\frac{6-2\sqrt{33}}{8}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+2\sqrt{33}}{2*4}=\frac{6+2\sqrt{33}}{8}
$