2.t(t-2)-6=9

Solution for 2.t(t-2)-6=9 equation:

2.t(t-2)-6=9

We move all terms to the left:

2.t(t-2)-6-(9)=0

We add all the numbers together, and all the variables

2.t(t-2)-15=0

We multiply parentheses

2t^2-4t-15=0

a = 2; b = -4; c = -15;
Δ = b2-4ac
Δ = -42-4·2·(-15)
Δ = 136
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:

$\sqrt{\Delta}=\sqrt{136}=\sqrt{4*34}=\sqrt{4}*\sqrt{34}=2\sqrt{34}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-2\sqrt{34}}{2*2}=\frac{4-2\sqrt{34}}{4}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+2\sqrt{34}}{2*2}=\frac{4+2\sqrt{34}}{4}
$