-3^2-15t+17=-6t^2

Solution for -3^2-15t+17=-6t^2 equation:

-3^2-15t+17=-6t^2

We move all terms to the left:

-3^2-15t+17-(-6t^2)=0

We add all the numbers together, and all the variables

-(-6t^2)-15t+8=0

We get rid of parentheses

6t^2-15t+8=0

a = 6; b = -15; c = +8;
Δ = b2-4ac
Δ = -152-4·6·8
Δ = 33
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-15)-\sqrt{33}}{2*6}=\frac{15-\sqrt{33}}{12}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-15)+\sqrt{33}}{2*6}=\frac{15+\sqrt{33}}{12}
$